Making use of a new and more general ansatz, we present the generalized algebraic method to uniformlyconstruct a series of new and general travelling wave solution for nonlinear partial differential equations. As an a...Making use of a new and more general ansatz, we present the generalized algebraic method to uniformlyconstruct a series of new and general travelling wave solution for nonlinear partial differential equations. As an applicationof the method, we choose a (1+1)-dimensional dispersive long wave equation to illustrate the method. As a result, wecan successfully obtain the solutions found by the method proposed by Fan [E. Fan, Comput. Phys. Commun. 153 (2003)17] and find other new and more general solutions at the same time, which include polynomial solutions, exponentialsolutions, rational solutions, triangular periodic wave solutions, hyperbolic and soliton solutions, Jacobi and Weierstrassdoubly periodic wave solutions.展开更多
A modified Zakharov-Kuznetsov equation for small but finite dustic waces in a magnetized votex-like ion distribution dusty plasma is obtained in this paper.It seems that there are instability for a soliton under hig...A modified Zakharov-Kuznetsov equation for small but finite dustic waces in a magnetized votex-like ion distribution dusty plasma is obtained in this paper.It seems that there are instability for a soliton under higher-order transverse perturbations in this system. There is a certain critical value 4λ0. If the ratio of the wave length of the higher-order perturbations to the width of the soliton is larger than this critical value, the solitary wave is unstable, otherwise it is stable.展开更多
Two new exact, rational and periodic wave solutions are derived for the two-dimensional Boussinesq equation. For the first solution it is obtained by performing an appropriate limiting procedure on the soliton solutio...Two new exact, rational and periodic wave solutions are derived for the two-dimensional Boussinesq equation. For the first solution it is obtained by performing an appropriate limiting procedure on the soliton solutions obtained by Hirota bilinear method. The second one in terms of Riemann theta function is explicitly presented by virtue of Hirota bilinear method and its asymptotic property is also analyzed in detail. Moreover, it is of interest to note that classical soliton solutions can be reduced from the periodic wave solutions.展开更多
A new three-component Camassa-Holm equation is introduced. This system is endowed with a structuresimilar to the Camassa-Holm equation. It has peakon solitons and conserves H^1-norm conservation law.
In this paper, we first consider exact solutions for Lienard equation with nonlinear terms of any order. Then,explicit exact bell and kink profile solitary-wave solutions for many nonlinear evolution equations are obt...In this paper, we first consider exact solutions for Lienard equation with nonlinear terms of any order. Then,explicit exact bell and kink profile solitary-wave solutions for many nonlinear evolution equations are obtained by means of results of the Lienard equation and proper deductions, which transform original partial differential equations into the Lienard one. These nonlinear equations include compound KdV, compound KdV-Burgers, generalized Boussinesq,generalized KP and Ginzburg-Landau equation. Some new solitary-wave solutions are found.展开更多
A(3+1)-dimensional Gross-Pitaevskii(GP)equation with time variable coefficients is considered,andis transformed into a standard nonlinear Schr(o|¨)dinger(NLS)equation.Exact solutions of the(3+1)D GP equationare c...A(3+1)-dimensional Gross-Pitaevskii(GP)equation with time variable coefficients is considered,andis transformed into a standard nonlinear Schr(o|¨)dinger(NLS)equation.Exact solutions of the(3+1)D GP equationare constructed via those of the NLS equation.By applying specific time-modulated nonlinearities,dispersions,andpotentials,the dynamics of the solutions can be controlled.Solitary and periodic wave solutions with snaking andbreathing behavior are reported.展开更多
The cubic-quintic nonlinear Schroedinger equation （CQNLS） plays important parts in the optical fiber and the nuclear hydrodynamics. By using the homogeneous balance principle, the bell type, kink type, algebraic sol...The cubic-quintic nonlinear Schroedinger equation （CQNLS） plays important parts in the optical fiber and the nuclear hydrodynamics. By using the homogeneous balance principle, the bell type, kink type, algebraic solitary waves, and trigonometric traveling waves for the cubic-quintic nonlinear Schroedinger equation with variable coefficients （vCQNLS） are derived with the aid of a set of subsidiary high-order ordinary differential equations （sub-equations for short）. The method used in this paper might help one to derive the exact solutions for the other high-order nonlinear evolution equations, and shows the new application of the homogeneous balance principle.展开更多
In this paper, exact and numerical solutions are calculated for discrete complex Ginzburg-Landau equation with initial condition by considering the modified Adomian decomposition method （mADM）, which is an efficient...In this paper, exact and numerical solutions are calculated for discrete complex Ginzburg-Landau equation with initial condition by considering the modified Adomian decomposition method （mADM）, which is an efficient method and does not need linearization, weak nonlinearity assumptions or perturbation theory. The numerical solutions are also compared with their corresponding analytical solutions. It is shown that a very good approximation is achieved with the analytical solutions. Finally, the modulational instability is investigated and the corresponding condition is given.展开更多
In this letter, we study discretized mKdV lattice equation by using a new generalized ansatz. As a result,many explicit rational exact solutions, including some new solitary wave solutions, are obtained by symbolic co...In this letter, we study discretized mKdV lattice equation by using a new generalized ansatz. As a result,many explicit rational exact solutions, including some new solitary wave solutions, are obtained by symbolic computation code Maple.展开更多
By using F-expansion method proposed recently, we derive the periodic wave solution expressed by Jacobi elliptic functions for Konopelchenko-Dubrovsky equation. In the limit case, the solitary wave solution and other ...By using F-expansion method proposed recently, we derive the periodic wave solution expressed by Jacobi elliptic functions for Konopelchenko-Dubrovsky equation. In the limit case, the solitary wave solution and other type of the traveling wave solutions are derived.展开更多
文摘Making use of a new and more general ansatz, we present the generalized algebraic method to uniformlyconstruct a series of new and general travelling wave solution for nonlinear partial differential equations. As an applicationof the method, we choose a (1+1)-dimensional dispersive long wave equation to illustrate the method. As a result, wecan successfully obtain the solutions found by the method proposed by Fan [E. Fan, Comput. Phys. Commun. 153 (2003)17] and find other new and more general solutions at the same time, which include polynomial solutions, exponentialsolutions, rational solutions, triangular periodic wave solutions, hyperbolic and soliton solutions, Jacobi and Weierstrassdoubly periodic wave solutions.
基金The project supported by National Natural Science Foundation of China under Grant Nos. 10575082 and 10247008 and the Scientific Research Foundation for the Returned 0verseas Chinese Scholars of the State Education Ministry
文摘A modified Zakharov-Kuznetsov equation for small but finite dustic waces in a magnetized votex-like ion distribution dusty plasma is obtained in this paper.It seems that there are instability for a soliton under higher-order transverse perturbations in this system. There is a certain critical value 4λ0. If the ratio of the wave length of the higher-order perturbations to the width of the soliton is larger than this critical value, the solitary wave is unstable, otherwise it is stable.
基金The project supported by National Natural Science Foundation of China under Grant No.10771196the Natural Science Foundation of Zhejiang Province under Grant No.Y605044
文摘Two new exact, rational and periodic wave solutions are derived for the two-dimensional Boussinesq equation. For the first solution it is obtained by performing an appropriate limiting procedure on the soliton solutions obtained by Hirota bilinear method. The second one in terms of Riemann theta function is explicitly presented by virtue of Hirota bilinear method and its asymptotic property is also analyzed in detail. Moreover, it is of interest to note that classical soliton solutions can be reduced from the periodic wave solutions.
基金Supported by National Natural Science Foundation of China under Grant Nos. 10671156 and 10671153
文摘A new three-component Camassa-Holm equation is introduced. This system is endowed with a structuresimilar to the Camassa-Holm equation. It has peakon solitons and conserves H^1-norm conservation law.
文摘In this paper, we first consider exact solutions for Lienard equation with nonlinear terms of any order. Then,explicit exact bell and kink profile solitary-wave solutions for many nonlinear evolution equations are obtained by means of results of the Lienard equation and proper deductions, which transform original partial differential equations into the Lienard one. These nonlinear equations include compound KdV, compound KdV-Burgers, generalized Boussinesq,generalized KP and Ginzburg-Landau equation. Some new solitary-wave solutions are found.
基金Supported by the National Natural Science Foundations of China under Grant Nos.10735030,10475055,10675065 and 90503006National Basic Research Program of China (973 Program 2007CB814800) and PCSIRT (IRT0734)+1 种基金the Research Fund of Postdoctoral of China under Grant No.20070410727Specialized Research Fund for the Doctoral Program of Higher Education under Grant No.20070248120
文摘A(3+1)-dimensional Gross-Pitaevskii(GP)equation with time variable coefficients is considered,andis transformed into a standard nonlinear Schr(o|¨)dinger(NLS)equation.Exact solutions of the(3+1)D GP equationare constructed via those of the NLS equation.By applying specific time-modulated nonlinearities,dispersions,andpotentials,the dynamics of the solutions can be controlled.Solitary and periodic wave solutions with snaking andbreathing behavior are reported.
基金The project supported in part by Natural Science Foundation of Henan Province of China under Grant No. 2006110002 and the Science Foundation of Henan University of Science and Technology under Grant No. 2004ZD002
文摘The cubic-quintic nonlinear Schroedinger equation （CQNLS） plays important parts in the optical fiber and the nuclear hydrodynamics. By using the homogeneous balance principle, the bell type, kink type, algebraic solitary waves, and trigonometric traveling waves for the cubic-quintic nonlinear Schroedinger equation with variable coefficients （vCQNLS） are derived with the aid of a set of subsidiary high-order ordinary differential equations （sub-equations for short）. The method used in this paper might help one to derive the exact solutions for the other high-order nonlinear evolution equations, and shows the new application of the homogeneous balance principle.
基金supported by National Natural Science Foundation of China under Grant No. 10672147
文摘In this paper, exact and numerical solutions are calculated for discrete complex Ginzburg-Landau equation with initial condition by considering the modified Adomian decomposition method （mADM）, which is an efficient method and does not need linearization, weak nonlinearity assumptions or perturbation theory. The numerical solutions are also compared with their corresponding analytical solutions. It is shown that a very good approximation is achieved with the analytical solutions. Finally, the modulational instability is investigated and the corresponding condition is given.
基金the National Key Basic Research Project of China under
文摘In this letter, we study discretized mKdV lattice equation by using a new generalized ansatz. As a result,many explicit rational exact solutions, including some new solitary wave solutions, are obtained by symbolic computation code Maple.
基金Supported by the Natural Science Foundation of Education Committee of Henan Province(2003110003)Supported by the Natural Science Foundation of Henan Province(0111050200)
文摘By using F-expansion method proposed recently, we derive the periodic wave solution expressed by Jacobi elliptic functions for Konopelchenko-Dubrovsky equation. In the limit case, the solitary wave solution and other type of the traveling wave solutions are derived.
