Making use of a new generalized ansatze and a proper transformation, we generalized the extended tanh-function method. Applying the generalized method with the aid of Maple, we consider some nonlinear evolution equati...Making use of a new generalized ansatze and a proper transformation, we generalized the extended tanh-function method. Applying the generalized method with the aid of Maple, we consider some nonlinear evolution equations.As a result, we can successfully recover the previously known solitary wave solutions that had been found by the extendedtanh-function method and other more sophisticated methods. More importantly, for some equations, we also obtain othernew and more general solutions at the same time. The results include kink-profile solitary-wave solutions, bell-profilesolitary-wave solutions, periodic wave solutions, rational solutions, singular solutions and new formal solutions.展开更多
A new generalized tanh function method is used for constructing exact travelling wave solutions of nonlinear partial differential equations in a unified way. The main idea of this method is to take full advantage of t...A new generalized tanh function method is used for constructing exact travelling wave solutions of nonlinear partial differential equations in a unified way. The main idea of this method is to take full advantage of the Riccati equation, which has more new solutions. More new multiple soliton-like solutions are obtained for the (3+ 1 )-dimensional Burgers equation with variable coefficients.展开更多
Based on the computerized symbolic system Mapte, a new generalized expansion method of Riccati equation for constructing non-travelling wave and coefficient functions' soliton-like solutions is presented by a new ...Based on the computerized symbolic system Mapte, a new generalized expansion method of Riccati equation for constructing non-travelling wave and coefficient functions' soliton-like solutions is presented by a new general ansatz. Making use of the method, we consider the (2+1)-dimensional breaking soliton equation, ut + buxxy + 4buvx+4buxv = O,uv=vx, and obtain rich new families of the exact solutions of the breaking sofiton equation, including then on-traveilin~ wave and constant function sofiton-like solutions, singular soliton-like solutions, and triangular function solutions.展开更多
In this paper, by using a further extended tanh method- and symbolic computation system, some new soliton-like and period form solutions of the dispersive long-wave equation in (2+l )-dimensional spaces are obtained.
By a simple transformation, we reduce the (2+1)-dimensional modified dispersive water-wave system to a simple nonlinear partial differential equation. In order to solve this equation by generalized tanh-function metho...By a simple transformation, we reduce the (2+1)-dimensional modified dispersive water-wave system to a simple nonlinear partial differential equation. In order to solve this equation by generalized tanh-function method, we only need to solve a simple system of first-order ordinary differential equations, and by doing so we can obtain many new soliton-like solutions which include the solutions obtained by using the conventional tanh-function method.展开更多
In this paper,we make use of a new generalized ansatz in the homogeneous balance method,the well-known Riccati equation and the symbolic computation to study a generalized hirota-Satsuma coupled KdsV system and a coup...In this paper,we make use of a new generalized ansatz in the homogeneous balance method,the well-known Riccati equation and the symbolic computation to study a generalized hirota-Satsuma coupled KdsV system and a coupled MKdv equation,respectively,As a result,numerous explicit exact solutions,comprising new solitary wave solutions,periodic wave solutions and the combined formal solitary wave solutions and periodic wave solutions,are obtained.展开更多
Applying the generalized method, which is a direct and unified algebraic method for constructing multipletravelling wave solutions of nonlinear partial differential equations (PDEs), and implementing in a computer alg...Applying the generalized method, which is a direct and unified algebraic method for constructing multipletravelling wave solutions of nonlinear partial differential equations (PDEs), and implementing in a computer algebraicsystem, we consider the generalized Zakharov-Kuzentsov equation with nonlinear terms of any order. As a result, wecan not only successfully recover the previously known travelling wave solutions found by existing various tanh methodsand other sophisticated methods, but also obtain some new formal solutions. The solutions obtained include kink-shapedsolitons, bell-shaped solitons, singular solitons, and periodic solutions.展开更多
This paper discusses the problem of positive periodic solutions for a class of nonlinearsecond order ordinary differential equations. By utilizing a fixed point theorem on cone, some exist-ence and multiplicity result...This paper discusses the problem of positive periodic solutions for a class of nonlinearsecond order ordinary differential equations. By utilizing a fixed point theorem on cone, some exist-ence and multiplicity results of positive periodic solutions are derived. Our results improve theoremsin the literature.展开更多
Based on our previous works and Lyapunov stability theory, this paper studies the generation and synchronization of N-scroll chaotic and hyperchaotic attractors in fourth-order systems. A fourth-order circuit, by intr...Based on our previous works and Lyapunov stability theory, this paper studies the generation and synchronization of N-scroll chaotic and hyperchaotic attractors in fourth-order systems. A fourth-order circuit, by introducing additional breakpoints in the modified Chua oscillator, is implemented for the study of generation and synchronization of N-scroll chaotic attractors.This confirms the consistency of theoretical calculation, numerical simulation and circuit experiment.Furthermore,we give a refined and extended study of generating and synchronizing N-scroll hyperchaotic attractors in the fourth-order MCK system and report the new theoretical result, which is verified by computer simulations.展开更多
The phenomenon of stochastic resonance (SR) in a bistable system driven by multiplicative and additive white noises and a periodic rectangular signal with a constant component is studied according to the theory of sig...The phenomenon of stochastic resonance (SR) in a bistable system driven by multiplicative and additive white noises and a periodic rectangular signal with a constant component is studied according to the theory of signal-to-noise ratio (SNR) in the adiabatic limit. The analytic expression of the SNR is obtained for arbitrary signal amplitude without being restricted to small amplitudes. We find that the effects of the multiplicative noise intensity D and additive noise intensity α on SNR are different: the SNR-α curve shows SR for almost the whole range of static asymmetry r, but the SNR-D curve only displays SR for some values of static asymmetry r. It is more sensitive to control SR through adjusting the additive noise intensity a than adjusting the multiplicative noise intensity D, when the asymmetry of bistable potential r is not too large. Moreover, the static asymmetry r decreases the SNR.展开更多
In this paper, we introduce a further generalized projective Riccati equation method and apply it to solve the (2+1)-dimensional modified dispersive water-wave system. Many new types of non-travelling wave solutions a...In this paper, we introduce a further generalized projective Riccati equation method and apply it to solve the (2+1)-dimensional modified dispersive water-wave system. Many new types of non-travelling wave solutions are obtained for this system.展开更多
In this paper,with the help of symbolic computation,a new Backlund transformation(BT)for a new generalized Zakharov-Kuznetsov equation with nonlinear term of any order,ut+aupux+bu2pux+γuxy+δuxxx+ρuxyy=0,is obtained...In this paper,with the help of symbolic computation,a new Backlund transformation(BT)for a new generalized Zakharov-Kuznetsov equation with nonlinear term of any order,ut+aupux+bu2pux+γuxy+δuxxx+ρuxyy=0,is obtained by using the homogeneous balance method.Based on the BT,some exact solutions are presented.展开更多
Flower image retrieval is a very important step for computer-aided plant species recognition. In this paper, we propose an efficient segmentation method based on color clustering and domain knowledge to extract flower...Flower image retrieval is a very important step for computer-aided plant species recognition. In this paper, we propose an efficient segmentation method based on color clustering and domain knowledge to extract flower regions from flower images. For flower retrieval, we use the color histogram of a flower region to characterize the color features of flower and two shape-based features sets, Centroid-Contour Distance (CCD) and Angle Code Histogram (ACH), to characterize the shape features of a flower contour. Experimental results showed that our flower region extraction method based on color clustering and domain knowledge can produce accurate flower regions. Flower retrieval results on a database of 885 flower images collected from 14 plant species showed that our Region-of-Interest (ROI) based retrieval approach using both color and shape features can perform better than a method based on the global color histogram proposed by Swain and Ballard (1991) and a method based on domain knowledge-driven segmentation and color names proposed by Das et al.(1999).展开更多
In this paper, a new modified extended tanh-function method is presented for constructing multiple soliton-like, periodic form and rational solutions of nonlinear evolution equations (NLEEs). This method is more power...In this paper, a new modified extended tanh-function method is presented for constructing multiple soliton-like, periodic form and rational solutions of nonlinear evolution equations (NLEEs). This method is more powerful thanthe extended tanh-function method [Phys. Lett. A277 (2000) 212] and the modified extended tanh-function method[Phys. Lett. A299 (2002) 179] Abundant new solutions of two physically important NLEEs are obtained by using thismethod and symbolic computation system Maple.展开更多
We generalize the algebraic method presented by Fan [J. Phys. A: Math. Gen. 36 (2003) 7009)] to uniformly construct a series of soliton-like solutions and double-like periodic solutions for nonlinear partial different...We generalize the algebraic method presented by Fan [J. Phys. A: Math. Gen. 36 (2003) 7009)] to uniformly construct a series of soliton-like solutions and double-like periodic solutions for nonlinear partial differential equations(NPDE). As an application of the method, we choose a (2+1)-dimensional asymmetric Nizhnik-Novikov-Vesselov equation and successfully construct new and more general solutions including a series of nontraveling wave and coefficient functions' soliton-like solutions, double-like periodic and trigonometric-like function solutions.展开更多
Abundant new soliton-like and period form solutions for certain (3+1)-dimensional physically important nonlinear evolution equations are obtained by using a further extended tanh method and symbolic computation system...Abundant new soliton-like and period form solutions for certain (3+1)-dimensional physically important nonlinear evolution equations are obtained by using a further extended tanh method and symbolic computation system, Maple.展开更多
In this paper, we consider Parallel Machines Scheduling with nonsimultaneous machine available time. We give the exact worst case performance bound of MLPT proposed by Lee. Furthermore, two other modified LPT algorith...In this paper, we consider Parallel Machines Scheduling with nonsimultaneous machine available time. We give the exact worst case performance bound of MLPT proposed by Lee. Furthermore, two other modified LPT algorithms are discussed. The paper is ended by numerical ex-periments of these algorithms.展开更多
Starting from Backlund transformation and using Cole-Hopf transformation, we reduce the integrable Broer-Kaup equations in (2+1)-dimensional spaces to a simple linear evolution equation with two arbitrary functions of...Starting from Backlund transformation and using Cole-Hopf transformation, we reduce the integrable Broer-Kaup equations in (2+1)-dimensional spaces to a simple linear evolution equation with two arbitrary functions of {x,t} and {y,t} in this paper. And we can obtain some new solutions of the original equations by investigating the simple nonlinear evolution equation, which include the solutions obtained by the variable separation approach.展开更多
Let T denote a tree with the diameter d(d≥2) and order n. Let P^*d,r,n-d-1denote the tree obtained by identifying the rth vertex of path Pd+l and the center of starKl,K1,n-d-1, where r = r(d) is the integer part abou...Let T denote a tree with the diameter d(d≥2) and order n. Let P^*d,r,n-d-1denote the tree obtained by identifying the rth vertex of path Pd+l and the center of starKl,K1,n-d-1, where r = r(d) is the integer part about d+2/2. Then p(T)≤ p(P^*d,r,n-d-1), andequality holds if and only if T≌P^*d,r。展开更多
文摘Making use of a new generalized ansatze and a proper transformation, we generalized the extended tanh-function method. Applying the generalized method with the aid of Maple, we consider some nonlinear evolution equations.As a result, we can successfully recover the previously known solitary wave solutions that had been found by the extendedtanh-function method and other more sophisticated methods. More importantly, for some equations, we also obtain othernew and more general solutions at the same time. The results include kink-profile solitary-wave solutions, bell-profilesolitary-wave solutions, periodic wave solutions, rational solutions, singular solutions and new formal solutions.
文摘A new generalized tanh function method is used for constructing exact travelling wave solutions of nonlinear partial differential equations in a unified way. The main idea of this method is to take full advantage of the Riccati equation, which has more new solutions. More new multiple soliton-like solutions are obtained for the (3+ 1 )-dimensional Burgers equation with variable coefficients.
文摘Based on the computerized symbolic system Mapte, a new generalized expansion method of Riccati equation for constructing non-travelling wave and coefficient functions' soliton-like solutions is presented by a new general ansatz. Making use of the method, we consider the (2+1)-dimensional breaking soliton equation, ut + buxxy + 4buvx+4buxv = O,uv=vx, and obtain rich new families of the exact solutions of the breaking sofiton equation, including then on-traveilin~ wave and constant function sofiton-like solutions, singular soliton-like solutions, and triangular function solutions.
文摘In this paper, by using a further extended tanh method- and symbolic computation system, some new soliton-like and period form solutions of the dispersive long-wave equation in (2+l )-dimensional spaces are obtained.
文摘By a simple transformation, we reduce the (2+1)-dimensional modified dispersive water-wave system to a simple nonlinear partial differential equation. In order to solve this equation by generalized tanh-function method, we only need to solve a simple system of first-order ordinary differential equations, and by doing so we can obtain many new soliton-like solutions which include the solutions obtained by using the conventional tanh-function method.
文摘In this paper,we make use of a new generalized ansatz in the homogeneous balance method,the well-known Riccati equation and the symbolic computation to study a generalized hirota-Satsuma coupled KdsV system and a coupled MKdv equation,respectively,As a result,numerous explicit exact solutions,comprising new solitary wave solutions,periodic wave solutions and the combined formal solitary wave solutions and periodic wave solutions,are obtained.
基金The project supported by National Natural Science Foundation of China under Grant No.10072013
the National Key Basic Research Development Program under Grant No.G1998030600
文摘Applying the generalized method, which is a direct and unified algebraic method for constructing multipletravelling wave solutions of nonlinear partial differential equations (PDEs), and implementing in a computer algebraicsystem, we consider the generalized Zakharov-Kuzentsov equation with nonlinear terms of any order. As a result, wecan not only successfully recover the previously known travelling wave solutions found by existing various tanh methodsand other sophisticated methods, but also obtain some new formal solutions. The solutions obtained include kink-shapedsolitons, bell-shaped solitons, singular solitons, and periodic solutions.
文摘This paper discusses the problem of positive periodic solutions for a class of nonlinearsecond order ordinary differential equations. By utilizing a fixed point theorem on cone, some exist-ence and multiplicity results of positive periodic solutions are derived. Our results improve theoremsin the literature.
文摘Based on our previous works and Lyapunov stability theory, this paper studies the generation and synchronization of N-scroll chaotic and hyperchaotic attractors in fourth-order systems. A fourth-order circuit, by introducing additional breakpoints in the modified Chua oscillator, is implemented for the study of generation and synchronization of N-scroll chaotic attractors.This confirms the consistency of theoretical calculation, numerical simulation and circuit experiment.Furthermore,we give a refined and extended study of generating and synchronizing N-scroll hyperchaotic attractors in the fourth-order MCK system and report the new theoretical result, which is verified by computer simulations.
文摘The phenomenon of stochastic resonance (SR) in a bistable system driven by multiplicative and additive white noises and a periodic rectangular signal with a constant component is studied according to the theory of signal-to-noise ratio (SNR) in the adiabatic limit. The analytic expression of the SNR is obtained for arbitrary signal amplitude without being restricted to small amplitudes. We find that the effects of the multiplicative noise intensity D and additive noise intensity α on SNR are different: the SNR-α curve shows SR for almost the whole range of static asymmetry r, but the SNR-D curve only displays SR for some values of static asymmetry r. It is more sensitive to control SR through adjusting the additive noise intensity a than adjusting the multiplicative noise intensity D, when the asymmetry of bistable potential r is not too large. Moreover, the static asymmetry r decreases the SNR.
文摘In this paper, we introduce a further generalized projective Riccati equation method and apply it to solve the (2+1)-dimensional modified dispersive water-wave system. Many new types of non-travelling wave solutions are obtained for this system.
文摘In this paper,with the help of symbolic computation,a new Backlund transformation(BT)for a new generalized Zakharov-Kuznetsov equation with nonlinear term of any order,ut+aupux+bu2pux+γuxy+δuxxx+ρuxyy=0,is obtained by using the homogeneous balance method.Based on the BT,some exact solutions are presented.
基金Project (Nos. 60302012 60202002) supported by the Nationa
Natural Science Foundation of China and the Research Grant
Council of the Hong Kong Special Administrative Region (No
PolyU 5119.01E) China
文摘Flower image retrieval is a very important step for computer-aided plant species recognition. In this paper, we propose an efficient segmentation method based on color clustering and domain knowledge to extract flower regions from flower images. For flower retrieval, we use the color histogram of a flower region to characterize the color features of flower and two shape-based features sets, Centroid-Contour Distance (CCD) and Angle Code Histogram (ACH), to characterize the shape features of a flower contour. Experimental results showed that our flower region extraction method based on color clustering and domain knowledge can produce accurate flower regions. Flower retrieval results on a database of 885 flower images collected from 14 plant species showed that our Region-of-Interest (ROI) based retrieval approach using both color and shape features can perform better than a method based on the global color histogram proposed by Swain and Ballard (1991) and a method based on domain knowledge-driven segmentation and color names proposed by Das et al.(1999).
文摘In this paper, a new modified extended tanh-function method is presented for constructing multiple soliton-like, periodic form and rational solutions of nonlinear evolution equations (NLEEs). This method is more powerful thanthe extended tanh-function method [Phys. Lett. A277 (2000) 212] and the modified extended tanh-function method[Phys. Lett. A299 (2002) 179] Abundant new solutions of two physically important NLEEs are obtained by using thismethod and symbolic computation system Maple.
文摘We generalize the algebraic method presented by Fan [J. Phys. A: Math. Gen. 36 (2003) 7009)] to uniformly construct a series of soliton-like solutions and double-like periodic solutions for nonlinear partial differential equations(NPDE). As an application of the method, we choose a (2+1)-dimensional asymmetric Nizhnik-Novikov-Vesselov equation and successfully construct new and more general solutions including a series of nontraveling wave and coefficient functions' soliton-like solutions, double-like periodic and trigonometric-like function solutions.
文摘Abundant new soliton-like and period form solutions for certain (3+1)-dimensional physically important nonlinear evolution equations are obtained by using a further extended tanh method and symbolic computation system, Maple.
文摘In this paper, we consider Parallel Machines Scheduling with nonsimultaneous machine available time. We give the exact worst case performance bound of MLPT proposed by Lee. Furthermore, two other modified LPT algorithms are discussed. The paper is ended by numerical ex-periments of these algorithms.
文摘Starting from Backlund transformation and using Cole-Hopf transformation, we reduce the integrable Broer-Kaup equations in (2+1)-dimensional spaces to a simple linear evolution equation with two arbitrary functions of {x,t} and {y,t} in this paper. And we can obtain some new solutions of the original equations by investigating the simple nonlinear evolution equation, which include the solutions obtained by the variable separation approach.
文摘Let T denote a tree with the diameter d(d≥2) and order n. Let P^*d,r,n-d-1denote the tree obtained by identifying the rth vertex of path Pd+l and the center of starKl,K1,n-d-1, where r = r(d) is the integer part about d+2/2. Then p(T)≤ p(P^*d,r,n-d-1), andequality holds if and only if T≌P^*d,r。
