Lump solutions are one of the most common solutions for nonlinear evolution equations.This study aspires to investigate the generalized Hietarintatype equation.We auspiciously provide multiple M-lump waves.On the othe...Lump solutions are one of the most common solutions for nonlinear evolution equations.This study aspires to investigate the generalized Hietarintatype equation.We auspiciously provide multiple M-lump waves.On the other hand,collision phenomena to multiple M-lump waves with soliton wave solutions are also provided.During the collision,the amplitude of the lump will change significantly over the processes,whereas the amplitude of the soliton will just minimally alter.As it is of paramount importance,we use suitable values of parameter to put out the physical features of the reported results through three dimensional and contour graphics.The results presented express physical features of lump and lump interaction phenomena of different kinds of nonlinear physical processes.Further,this study serves to enrich nonlinear dynamics and provide insight into how nonlinear waves propagate.展开更多
In this paper,we set up dynamic solitary perturb solutions of a unidirectional stochastic longitudinal wave equation in a magneto-electro-elastic annular bar by a feasible,useful,and influential method named the dual(...In this paper,we set up dynamic solitary perturb solutions of a unidirectional stochastic longitudinal wave equation in a magneto-electro-elastic annular bar by a feasible,useful,and influential method named the dual(G’/G,1/G)-expansion method.Computer software,like Mathematica,is used to complete this discussion.The obtained solutions of the proposed equation are classified into trigonometric,hyperbolic,and rational types which play an important role in searching for numerous scientific events.The technique employed here is an extension of the(G’/G)-expansion technique for finding all previously discovered solutions.To illustrate our findings more clearly,we provide 2D and 3D charts of the various recovery methods.We then contrasted our findings with those of past solutions.The graphical illustrations of the acquired solutions are singular periodic solitons and kink solitons which are added at the end of this paper.展开更多
The principal objective of this article is to construct new and further exact soliton solutions of the(2+1)-dimensional Heisenberg ferromagnetic spin chain equation which investigates the nonlinear dynamics of magnets...The principal objective of this article is to construct new and further exact soliton solutions of the(2+1)-dimensional Heisenberg ferromagnetic spin chain equation which investigates the nonlinear dynamics of magnets and explains their ordering in ferromagnetic materials.These solutions are exerted via the new extended FAN sub-equation method.We successfully obtain dark,bright,combined bright-dark,combined dark-singular,periodic,periodic singular,and elliptic wave solutions to this equation which are interesting classes of nonlinear excitation presenting spin dynamics in classical and semi-classical continuum Heisenberg systems.3D figures are illustrated under an appropriate selection of parameters.The applied technique is suitable to be used in gaining the exact solutions of most nonlinear partial/fractional differential equations which appear in complex phenomena.展开更多
The prime objective of this paper is to explore the new exact soliton solutions to the higher-dimensional nonlinear Fokas equation and(2+1)-dimensional breaking soliton equations via a generalized exponential rational...The prime objective of this paper is to explore the new exact soliton solutions to the higher-dimensional nonlinear Fokas equation and(2+1)-dimensional breaking soliton equations via a generalized exponential rational function(GERF) method. Many different kinds of exact soliton solution are obtained, all of which are completely novel and have never been reported in the literature before. The dynamical behaviors of some obtained exact soliton solutions are also demonstrated by a choice of appropriate values of the free constants that aid in understanding the nonlinear complex phenomena of such equations. These exact soliton solutions are observed in the shapes of different dynamical structures of localized solitary wave solutions, singular-form solitons, single solitons,double solitons, triple solitons, bell-shaped solitons, combo singular solitons, breather-type solitons,elastic interactions between triple solitons and kink waves, and elastic interactions between diverse solitons and kink waves. Because of the reduction in symbolic computation work and the additional constructed closed-form solutions, it is observed that the suggested technique is effective, robust, and straightforward. Moreover, several other types of higher-dimensional nonlinear evolution equation can be solved using the powerful GERF technique.展开更多
The(3+1)-dimensional Zakharov–Kuznetsov(ZK) and the new extended quantum ZK equations are functional to decipher the dense quantum plasma, ion-acoustic waves, electron thermal energy,ion plasma, quantum acoustic wave...The(3+1)-dimensional Zakharov–Kuznetsov(ZK) and the new extended quantum ZK equations are functional to decipher the dense quantum plasma, ion-acoustic waves, electron thermal energy,ion plasma, quantum acoustic waves, and quantum Langmuir waves. The enhanced modified simple equation(EMSE) method is a substantial approach to determine competent solutions and in this article, we have constructed standard, illustrative, rich structured and further comprehensive soliton solutions via this method. The solutions are ascertained as the integration of exponential, hyperbolic,trigonometric and rational functions and formulate the bright solitons, periodic, compacton, bellshape, parabolic shape, singular periodic, plane shape and some new type of solitons. It is worth noting that the wave profile varies as the physical and subsidiary parameters change. The standard and advanced soliton solutions may be useful to assist in describing the physical phenomena previously mentioned. To open out the inward structure of the tangible incidents, we have portrayed the three-dimensional, contour plot, and two-dimensional graphs for different parametric values. The attained results demonstrate the EMSE technique for extracting soliton solutions to nonlinear evolution equations is efficient, compatible and reliable in nonlinear science and engineering.展开更多
This treatise analyzes the coupled nonlinear system of the model for the ion sound and Langmuir waves.The modified(G'/G)-expansion procedure is utilized to raise new closed-form wave solutions.Those solutions are ...This treatise analyzes the coupled nonlinear system of the model for the ion sound and Langmuir waves.The modified(G'/G)-expansion procedure is utilized to raise new closed-form wave solutions.Those solutions are investigated through hyperbolic,trigonometric and rational function.The graphical design makes the dynamics of the equations noticeable.It provides the mathematical foundation in diverse sectors of underwater acoustics,electromagnetic wave propagation,design of specific optoelectronic devices and physics quantum mechanics.Herein,we concluded that the studied approach is advanced,meaningful and significant in implementing many solutions of several nonlinear partial differential equations occurring in applied sciences.展开更多
This study investigates the perturbed Chen–Lee–Liu model that represents the propagation of an optical pulse in plasma and optical fiber.The generalized exponential rational function method is used for this purpose....This study investigates the perturbed Chen–Lee–Liu model that represents the propagation of an optical pulse in plasma and optical fiber.The generalized exponential rational function method is used for this purpose.As a result,we obtain some non-trivial solutions such as the optical singular,periodic,hyperbolic,exponential,trigonometric soliton solutions.We aim to express the pulse propagation of the generated solutions,by taking specific values for the free parameters existed in the obtained solutions.The obtained results show that the generalized exponential rational function technique is applicable,simple and effective to get the solutions of nonlinear engineering and physical problems.Moreover,the acquired solutions display rich dynamical evolutions that are important in practical applications.展开更多
文摘Lump solutions are one of the most common solutions for nonlinear evolution equations.This study aspires to investigate the generalized Hietarintatype equation.We auspiciously provide multiple M-lump waves.On the other hand,collision phenomena to multiple M-lump waves with soliton wave solutions are also provided.During the collision,the amplitude of the lump will change significantly over the processes,whereas the amplitude of the soliton will just minimally alter.As it is of paramount importance,we use suitable values of parameter to put out the physical features of the reported results through three dimensional and contour graphics.The results presented express physical features of lump and lump interaction phenomena of different kinds of nonlinear physical processes.Further,this study serves to enrich nonlinear dynamics and provide insight into how nonlinear waves propagate.
文摘In this paper,we set up dynamic solitary perturb solutions of a unidirectional stochastic longitudinal wave equation in a magneto-electro-elastic annular bar by a feasible,useful,and influential method named the dual(G’/G,1/G)-expansion method.Computer software,like Mathematica,is used to complete this discussion.The obtained solutions of the proposed equation are classified into trigonometric,hyperbolic,and rational types which play an important role in searching for numerous scientific events.The technique employed here is an extension of the(G’/G)-expansion technique for finding all previously discovered solutions.To illustrate our findings more clearly,we provide 2D and 3D charts of the various recovery methods.We then contrasted our findings with those of past solutions.The graphical illustrations of the acquired solutions are singular periodic solitons and kink solitons which are added at the end of this paper.
基金the Basic Science Research Unit,Scientific Research Deanship at Majmaah University,project number RGP-2019-4。
文摘The principal objective of this article is to construct new and further exact soliton solutions of the(2+1)-dimensional Heisenberg ferromagnetic spin chain equation which investigates the nonlinear dynamics of magnets and explains their ordering in ferromagnetic materials.These solutions are exerted via the new extended FAN sub-equation method.We successfully obtain dark,bright,combined bright-dark,combined dark-singular,periodic,periodic singular,and elliptic wave solutions to this equation which are interesting classes of nonlinear excitation presenting spin dynamics in classical and semi-classical continuum Heisenberg systems.3D figures are illustrated under an appropriate selection of parameters.The applied technique is suitable to be used in gaining the exact solutions of most nonlinear partial/fractional differential equations which appear in complex phenomena.
基金funded by the Science and Engineering Research Board,SERB-DST,India,under project scheme MATRICS(MTR/2020/000531)。
文摘The prime objective of this paper is to explore the new exact soliton solutions to the higher-dimensional nonlinear Fokas equation and(2+1)-dimensional breaking soliton equations via a generalized exponential rational function(GERF) method. Many different kinds of exact soliton solution are obtained, all of which are completely novel and have never been reported in the literature before. The dynamical behaviors of some obtained exact soliton solutions are also demonstrated by a choice of appropriate values of the free constants that aid in understanding the nonlinear complex phenomena of such equations. These exact soliton solutions are observed in the shapes of different dynamical structures of localized solitary wave solutions, singular-form solitons, single solitons,double solitons, triple solitons, bell-shaped solitons, combo singular solitons, breather-type solitons,elastic interactions between triple solitons and kink waves, and elastic interactions between diverse solitons and kink waves. Because of the reduction in symbolic computation work and the additional constructed closed-form solutions, it is observed that the suggested technique is effective, robust, and straightforward. Moreover, several other types of higher-dimensional nonlinear evolution equation can be solved using the powerful GERF technique.
文摘The(3+1)-dimensional Zakharov–Kuznetsov(ZK) and the new extended quantum ZK equations are functional to decipher the dense quantum plasma, ion-acoustic waves, electron thermal energy,ion plasma, quantum acoustic waves, and quantum Langmuir waves. The enhanced modified simple equation(EMSE) method is a substantial approach to determine competent solutions and in this article, we have constructed standard, illustrative, rich structured and further comprehensive soliton solutions via this method. The solutions are ascertained as the integration of exponential, hyperbolic,trigonometric and rational functions and formulate the bright solitons, periodic, compacton, bellshape, parabolic shape, singular periodic, plane shape and some new type of solitons. It is worth noting that the wave profile varies as the physical and subsidiary parameters change. The standard and advanced soliton solutions may be useful to assist in describing the physical phenomena previously mentioned. To open out the inward structure of the tangible incidents, we have portrayed the three-dimensional, contour plot, and two-dimensional graphs for different parametric values. The attained results demonstrate the EMSE technique for extracting soliton solutions to nonlinear evolution equations is efficient, compatible and reliable in nonlinear science and engineering.
文摘This treatise analyzes the coupled nonlinear system of the model for the ion sound and Langmuir waves.The modified(G'/G)-expansion procedure is utilized to raise new closed-form wave solutions.Those solutions are investigated through hyperbolic,trigonometric and rational function.The graphical design makes the dynamics of the equations noticeable.It provides the mathematical foundation in diverse sectors of underwater acoustics,electromagnetic wave propagation,design of specific optoelectronic devices and physics quantum mechanics.Herein,we concluded that the studied approach is advanced,meaningful and significant in implementing many solutions of several nonlinear partial differential equations occurring in applied sciences.
文摘This study investigates the perturbed Chen–Lee–Liu model that represents the propagation of an optical pulse in plasma and optical fiber.The generalized exponential rational function method is used for this purpose.As a result,we obtain some non-trivial solutions such as the optical singular,periodic,hyperbolic,exponential,trigonometric soliton solutions.We aim to express the pulse propagation of the generated solutions,by taking specific values for the free parameters existed in the obtained solutions.The obtained results show that the generalized exponential rational function technique is applicable,simple and effective to get the solutions of nonlinear engineering and physical problems.Moreover,the acquired solutions display rich dynamical evolutions that are important in practical applications.
