To seek new infinite sequence soliton-like exact solutions to nonlinear evolution equations （NEE（s））, by developing two characteristics of construction and mechanization on auxiliary equation method, the second ki...To seek new infinite sequence soliton-like exact solutions to nonlinear evolution equations （NEE（s））, by developing two characteristics of construction and mechanization on auxiliary equation method, the second kind of elliptie equation is highly studied and new type solutions and Backlund transformation are obtained. Then （2＋ l ）-dimensional breaking soliton equation is chosen as an example and its infinite sequence soliton-like exact solutions are constructed with the help of symbolic computation system Mathematica, which include infinite sequence smooth soliton-like solutions of Jacobi elliptic type, infinite sequence compact soliton solutions of Jacobi elliptic type and infinite sequence peak soliton solutions of exponential function type and triangular function type.展开更多
A spherical Kadomtsev-Petviashvili （SKP） equation for dust acoustic or ion-acoustic waves is studied. Similarity reductions of the SKP equation are obtained with the one-parameter （ε） Lie group of infinitesimal t...A spherical Kadomtsev-Petviashvili （SKP） equation for dust acoustic or ion-acoustic waves is studied. Similarity reductions of the SKP equation are obtained with the one-parameter （ε） Lie group of infinitesimal transformations and Clarkson-Kruskal direct method, The SKP equation is also solved with a generalized tanh function method.展开更多
In this paper, the generalized ranch function method is extended to （2＋1）-dimensianal canonical generalized KP （CGKP） equation with variable coetfficients. Taking advantage of the Riccati equation, many explicit ...In this paper, the generalized ranch function method is extended to （2＋1）-dimensianal canonical generalized KP （CGKP） equation with variable coetfficients. Taking advantage of the Riccati equation, many explicit exact solutions, which contain multiple soliton-like and periodic solutions, are obtained for the （2＋1）-dimensional OGKP equation with variable coetffcients.展开更多
Instead of the usual Hirota ansatz,i.e.,the functions in bilinear equations being chosen as exponentialtypes,a generalized Hirota ansatz is proposed for a (3+1)-dimensional nonlinear evolution equation.Based on theres...Instead of the usual Hirota ansatz,i.e.,the functions in bilinear equations being chosen as exponentialtypes,a generalized Hirota ansatz is proposed for a (3+1)-dimensional nonlinear evolution equation.Based on theresulting generalized Hirota ansatz,a family of new explicit solutions for the equation are derived.展开更多
In the present research work, we have obtained the exact spherical symmetric solutions of Heisenberg-Ivanenko nonlinear spinor field equations in the Gravitational Theory. The nonlinearity in the spinor Lagrangian is ...In the present research work, we have obtained the exact spherical symmetric solutions of Heisenberg-Ivanenko nonlinear spinor field equations in the Gravitational Theory. The nonlinearity in the spinor Lagrangian is given by an arbitrary function which depends on the invariant generated from the bilinear spinor form <em>I<sub>s</sub></em><sub> </sub>= <em>S</em><sup>2</sup>. We admit the static spherical symmetric metric. It is shown that a soliton-like configuration has a localized energy density and a finite total energy. In addition, The total charge and total spin are also finite. Role of the metric<em> i.e.</em> the proper gravitational field of elementary particles in the formation of the field configurations with limited total energy, spin and charge has been examined by solving the field equations in flat space-time. It has been established that the obtained solutions are soliton-like configuration with bounded energy density and finite total energy. In order to clarify the role of the nonlinearity in this model, we have obtained exact statical symmetric solutions to the above spinor field equations in the linear case corresponding to Dirac’s linear equation. It is proved that soliton-like solutions are absent.展开更多
By the application of the extended tanh method and the symbolic computation system Mathematica, new soliton-like solutions are obtained for the combined KdV and mKdV (KdV-mKdV) equation.
In this letter, we construct a kind of new Darboux transformation for the （1＋1）-dimensional higher-order Broer-Kaup （HBK） system with the help of a gauge transformation of a spectral problem. By applying this new...In this letter, we construct a kind of new Darboux transformation for the （1＋1）-dimensional higher-order Broer-Kaup （HBK） system with the help of a gauge transformation of a spectral problem. By applying this new Darboux transformation, some new soliton-like solutions of the （1＋1）-dimensional HBK system are obtained.展开更多
This paper deals with an extension of a previous work [Gravitation & Cosmology, Vol. 4, 1998, pp 107-113] to exact spherical symmetric solutions to the spinor field equations with nonlinear terms which are arbitra...This paper deals with an extension of a previous work [Gravitation & Cosmology, Vol. 4, 1998, pp 107-113] to exact spherical symmetric solutions to the spinor field equations with nonlinear terms which are arbitrary functions of S=ψψ, taking into account their own gravitational field. Equations with power and polynomial nonlinearities are studied in detail. It is shown that the initial set of the Einstein and spinor field equations with a power nonlinearity has regular solutions with spinor field localized energy and charge densities. The total energy and charge are finite. Besides, exact solutions, including soliton-like solutions, to the spinor field equations are also obtained in flat space-time.展开更多
The present research work is considered as part II of the previous work entitled [Plane Symmetric Solutions to the Nonlinear Spinor Field Equations in General Relativity Theory, jmp, 2019, 10, 1222-1234]. Here, we opt...The present research work is considered as part II of the previous work entitled [Plane Symmetric Solutions to the Nonlinear Spinor Field Equations in General Relativity Theory, jmp, 2019, 10, 1222-1234]. Here, we opt for the static spherical symmetric metric. In this metric, we have obtained spherical symmetric soliton-like solutions to the spinor field equations with nonlinear terms, which are arbitrary functions of , taking into account the proper gravitational field of elementary particles. Equations with power and polynomial nonlinearities are investigated in detail. It is shown that the initial set of the Einstein and spinor field equations with a power-law nonlinearity possess regular solutions with a localized energy density of the spinor field only if we consider massless particle without losing the generality (m = 0). In this case, a soliton-like configuration has negative energy. In order to define the role of the nonlinearity and the own gravitational field of the elementary particles in this model, we have obtained exact static symmetric solutions to the above spinor field equations in the linear case by considering Dirac’s equations and in flat space-time. It is proved that soliton-like solutions are absent in the linear case. But in flat space-time soliton-like configurations exist and have positive total energy.展开更多
The truncated expansion method for finding explicit and exact soliton-like solution of variable coefficient nonlinear evolution equation was described. The crucial idea of the method was first the assumption that coef...The truncated expansion method for finding explicit and exact soliton-like solution of variable coefficient nonlinear evolution equation was described. The crucial idea of the method was first the assumption that coefficients of the truncated expansion formal solution are functions of time satisfying a set of algebraic equations, and then a set of ordinary different equations of undetermined functions that can be easily integrated were obtained. The simplicity and effectiveness of the method by application to a general variable coefficient KdV-MKdV equation with three arbitrary functions of time is illustrated.展开更多
This paper studies the evolution of wave in the system of a pure anharmonic lattice with a double well on-site potential by numerical calculation. It finds that an initial distribution of static or moving wave can evo...This paper studies the evolution of wave in the system of a pure anharmonic lattice with a double well on-site potential by numerical calculation. It finds that an initial distribution of static or moving wave can evolve into two travelling soliton-like trains with contrary directions and a region of oscillation in this lattice system. It presents that some cases with cosine-square-shape and Gaussian-shape initial distribution of static or moving wave will produce ordered soliton-like train. Careful numerical observation shows that the centre oscillation region in this system may act as a resource of generating soliton-like train.展开更多
In this paper, the Wick-type stochastic mKdV equation is researched. Many Wick-type stochastic solitonlike solutions are given via Hermite transformation and further generalized projective Riccati equation method.
The (2+1)-dimensional breaking soliton equation describes the interaction of a Riemann wave propagating along the y-axis with a long wave along the x-axis. In this paper, with the aid of symbolic computation, six kind...The (2+1)-dimensional breaking soliton equation describes the interaction of a Riemann wave propagating along the y-axis with a long wave along the x-axis. In this paper, with the aid of symbolic computation, six kinds of new special exact soltion-like solutions of (2+1)-dimensional breaking soliton equation are obtained by using some general transformations and the further generalized projective Riccati equation method.展开更多
By using the further extended tanh method [Phys. Lett. A 307 （2003） 269; Chaos, Solitons ＆ Fractals 17 （2003） 669] to the Broer-Kaup system with variable coefficients, abundant new soliton-like solutions and mult...By using the further extended tanh method [Phys. Lett. A 307 （2003） 269; Chaos, Solitons ＆ Fractals 17 （2003） 669] to the Broer-Kaup system with variable coefficients, abundant new soliton-like solutions and multl-solitonlike solutions are derived. Based on the derived multi-soliton-like solutions which contain arbitrary functions, some interesting multi-soliton structures are revealed.展开更多
We study the Peregrine rogue waves within the framework of Derivative Nonlinear Schrödinger equation, which is used to describe the propagation of Alfven waves in plasma physics and sub-picosecond or femtosecond ...We study the Peregrine rogue waves within the framework of Derivative Nonlinear Schrödinger equation, which is used to describe the propagation of Alfven waves in plasma physics and sub-picosecond or femtosecond pulses in nonlinear optics. The interaction and degeneration of two soliton-like solutions and its relations for the breather solution have been analyzed. The Peregrine rogue waves have been considered from the two kinds of formation processes: it can be generated through the limitation of the infinitely large period of the breather solutions, and it can be interpreted as the soliton-like solutions with different polarities. As a special example, a special Peregrine rogue wave is generated by a breather solution and phase solution, which is given by the trivial seed (zero solution).展开更多
The characteristics of N-type accumulation-mode MOS (NMOS) varactors line periodically loaded with resonant tunneling diodes (RTDs) are used for soliton-like pulses generation and shaping. The problem of wide pulse br...The characteristics of N-type accumulation-mode MOS (NMOS) varactors line periodically loaded with resonant tunneling diodes (RTDs) are used for soliton-like pulses generation and shaping. The problem of wide pulse breaking up into multiple pulses rather than a single is solved. Applying perturbative analysis, we show that the dynamics of the nonlinear transmission line (NLTL) is reduced to expanded Korteweg-de Vries (KdV) equation. Moreover, numerical integration of nonlinear differential and difference equations that result from the mathematical analysis of the line is discussed. As results, NLTL can simultaneously sharpen both leading and trailing of pulse edges and one could obtain a rising and sharpening step pulse.展开更多
基金Supported by the Natural Natural Science Foundation of China under Grant No.10461006the Science Research Foundation of Institution of Higher Education of Inner Mongolia Autonomous Region,China under Grant No.NJZZ07031the Natural Science Foundation of Inner Mongolia Autonomous Region,China under Grant No.2010MS0111
文摘To seek new infinite sequence soliton-like exact solutions to nonlinear evolution equations （NEE（s））, by developing two characteristics of construction and mechanization on auxiliary equation method, the second kind of elliptie equation is highly studied and new type solutions and Backlund transformation are obtained. Then （2＋ l ）-dimensional breaking soliton equation is chosen as an example and its infinite sequence soliton-like exact solutions are constructed with the help of symbolic computation system Mathematica, which include infinite sequence smooth soliton-like solutions of Jacobi elliptic type, infinite sequence compact soliton solutions of Jacobi elliptic type and infinite sequence peak soliton solutions of exponential function type and triangular function type.
基金The project supported by the Tian Yuan Fund for Mathematics under Grand No 10426007, the Key Project of the Ministry of Education under Grant No. 106033, and National Science Foundation of China under.Grants Nos, 60372095 and 10272017. YTG would like to acknowledge the Cheung Kong Scholars Programme of the Ministry of Educ＇atlon of China and Li Ka Shing Foundation of Hong Kong
文摘A spherical Kadomtsev-Petviashvili （SKP） equation for dust acoustic or ion-acoustic waves is studied. Similarity reductions of the SKP equation are obtained with the one-parameter （ε） Lie group of infinitesimal transformations and Clarkson-Kruskal direct method, The SKP equation is also solved with a generalized tanh function method.
基金The project supported by the Natural Science Foundation of Shandong Province under Grant Nos. 2004zx16 and Q2005A01
文摘In this paper, the generalized ranch function method is extended to （2＋1）-dimensianal canonical generalized KP （CGKP） equation with variable coetfficients. Taking advantage of the Riccati equation, many explicit exact solutions, which contain multiple soliton-like and periodic solutions, are obtained for the （2＋1）-dimensional OGKP equation with variable coetffcients.
文摘Instead of the usual Hirota ansatz,i.e.,the functions in bilinear equations being chosen as exponentialtypes,a generalized Hirota ansatz is proposed for a (3+1)-dimensional nonlinear evolution equation.Based on theresulting generalized Hirota ansatz,a family of new explicit solutions for the equation are derived.
文摘In the present research work, we have obtained the exact spherical symmetric solutions of Heisenberg-Ivanenko nonlinear spinor field equations in the Gravitational Theory. The nonlinearity in the spinor Lagrangian is given by an arbitrary function which depends on the invariant generated from the bilinear spinor form <em>I<sub>s</sub></em><sub> </sub>= <em>S</em><sup>2</sup>. We admit the static spherical symmetric metric. It is shown that a soliton-like configuration has a localized energy density and a finite total energy. In addition, The total charge and total spin are also finite. Role of the metric<em> i.e.</em> the proper gravitational field of elementary particles in the formation of the field configurations with limited total energy, spin and charge has been examined by solving the field equations in flat space-time. It has been established that the obtained solutions are soliton-like configuration with bounded energy density and finite total energy. In order to clarify the role of the nonlinearity in this model, we have obtained exact statical symmetric solutions to the above spinor field equations in the linear case corresponding to Dirac’s linear equation. It is proved that soliton-like solutions are absent.
文摘By the application of the extended tanh method and the symbolic computation system Mathematica, new soliton-like solutions are obtained for the combined KdV and mKdV (KdV-mKdV) equation.
基金The project partially supported by the State Key Basic Pesearch Program of China under Grant No. 2004CB318000
文摘In this letter, we construct a kind of new Darboux transformation for the （1＋1）-dimensional higher-order Broer-Kaup （HBK） system with the help of a gauge transformation of a spectral problem. By applying this new Darboux transformation, some new soliton-like solutions of the （1＋1）-dimensional HBK system are obtained.
文摘This paper deals with an extension of a previous work [Gravitation & Cosmology, Vol. 4, 1998, pp 107-113] to exact spherical symmetric solutions to the spinor field equations with nonlinear terms which are arbitrary functions of S=ψψ, taking into account their own gravitational field. Equations with power and polynomial nonlinearities are studied in detail. It is shown that the initial set of the Einstein and spinor field equations with a power nonlinearity has regular solutions with spinor field localized energy and charge densities. The total energy and charge are finite. Besides, exact solutions, including soliton-like solutions, to the spinor field equations are also obtained in flat space-time.
文摘The present research work is considered as part II of the previous work entitled [Plane Symmetric Solutions to the Nonlinear Spinor Field Equations in General Relativity Theory, jmp, 2019, 10, 1222-1234]. Here, we opt for the static spherical symmetric metric. In this metric, we have obtained spherical symmetric soliton-like solutions to the spinor field equations with nonlinear terms, which are arbitrary functions of , taking into account the proper gravitational field of elementary particles. Equations with power and polynomial nonlinearities are investigated in detail. It is shown that the initial set of the Einstein and spinor field equations with a power-law nonlinearity possess regular solutions with a localized energy density of the spinor field only if we consider massless particle without losing the generality (m = 0). In this case, a soliton-like configuration has negative energy. In order to define the role of the nonlinearity and the own gravitational field of the elementary particles in this model, we have obtained exact static symmetric solutions to the above spinor field equations in the linear case by considering Dirac’s equations and in flat space-time. It is proved that soliton-like solutions are absent in the linear case. But in flat space-time soliton-like configurations exist and have positive total energy.
基金the Natural Science Foundation of Zhejiang Province of China (100039)
文摘The truncated expansion method for finding explicit and exact soliton-like solution of variable coefficient nonlinear evolution equation was described. The crucial idea of the method was first the assumption that coefficients of the truncated expansion formal solution are functions of time satisfying a set of algebraic equations, and then a set of ordinary different equations of undetermined functions that can be easily integrated were obtained. The simplicity and effectiveness of the method by application to a general variable coefficient KdV-MKdV equation with three arbitrary functions of time is illustrated.
基金Project supported by the Natural Science Foundation of Hunan Province, China （Grant Nos 04JJ3078 and 04JJ6029）.
文摘This paper studies the evolution of wave in the system of a pure anharmonic lattice with a double well on-site potential by numerical calculation. It finds that an initial distribution of static or moving wave can evolve into two travelling soliton-like trains with contrary directions and a region of oscillation in this lattice system. It presents that some cases with cosine-square-shape and Gaussian-shape initial distribution of static or moving wave will produce ordered soliton-like train. Careful numerical observation shows that the centre oscillation region in this system may act as a resource of generating soliton-like train.
基金国家重点基础研究发展计划(973计划)，the National Natural Science Foundation of China under
文摘In this paper, the Wick-type stochastic mKdV equation is researched. Many Wick-type stochastic solitonlike solutions are given via Hermite transformation and further generalized projective Riccati equation method.
文摘The (2+1)-dimensional breaking soliton equation describes the interaction of a Riemann wave propagating along the y-axis with a long wave along the x-axis. In this paper, with the aid of symbolic computation, six kinds of new special exact soltion-like solutions of (2+1)-dimensional breaking soliton equation are obtained by using some general transformations and the further generalized projective Riccati equation method.
基金中国博士后科学基金，National Key Basic Research Project of China
文摘By using the further extended tanh method [Phys. Lett. A 307 （2003） 269; Chaos, Solitons ＆ Fractals 17 （2003） 669] to the Broer-Kaup system with variable coefficients, abundant new soliton-like solutions and multl-solitonlike solutions are derived. Based on the derived multi-soliton-like solutions which contain arbitrary functions, some interesting multi-soliton structures are revealed.
文摘We study the Peregrine rogue waves within the framework of Derivative Nonlinear Schrödinger equation, which is used to describe the propagation of Alfven waves in plasma physics and sub-picosecond or femtosecond pulses in nonlinear optics. The interaction and degeneration of two soliton-like solutions and its relations for the breather solution have been analyzed. The Peregrine rogue waves have been considered from the two kinds of formation processes: it can be generated through the limitation of the infinitely large period of the breather solutions, and it can be interpreted as the soliton-like solutions with different polarities. As a special example, a special Peregrine rogue wave is generated by a breather solution and phase solution, which is given by the trivial seed (zero solution).
文摘The characteristics of N-type accumulation-mode MOS (NMOS) varactors line periodically loaded with resonant tunneling diodes (RTDs) are used for soliton-like pulses generation and shaping. The problem of wide pulse breaking up into multiple pulses rather than a single is solved. Applying perturbative analysis, we show that the dynamics of the nonlinear transmission line (NLTL) is reduced to expanded Korteweg-de Vries (KdV) equation. Moreover, numerical integration of nonlinear differential and difference equations that result from the mathematical analysis of the line is discussed. As results, NLTL can simultaneously sharpen both leading and trailing of pulse edges and one could obtain a rising and sharpening step pulse.
