In this paper, we study peakon, cuspon, smooth soliton and periodic cusp wave of the generalized Schr6dinger-Boussinesq equations. Based on the method of dynamical systems, the generalized Schr6dinger-Boussinesq equat...In this paper, we study peakon, cuspon, smooth soliton and periodic cusp wave of the generalized Schr6dinger-Boussinesq equations. Based on the method of dynamical systems, the generalized Schr6dinger-Boussinesq equations are shown to have new the parametric representations of peakon, cuspon, smooth solRon and periodic cusp wave solutions. Under different parametric conditions, various sufficient conditions to guarantee the existence of the above solutions are g/van.展开更多
For the (2 + 1)-dimensional nonlinear dispersive Boussinesq equation, by using the bifurcation theory of planar dynamical systems to study its corresponding traveling wave system, the bifurcations and phase portraits ...For the (2 + 1)-dimensional nonlinear dispersive Boussinesq equation, by using the bifurcation theory of planar dynamical systems to study its corresponding traveling wave system, the bifurcations and phase portraits of the regular system are obtained. Under different parametric conditions, various sufficient conditions to guarantee the existence of analytical and non-analytical solutions of the singular system are given by using singular traveling wave theory. For certain special cases, some explicit and exact parametric representations of traveling wave solutions are derived such as analytical periodic waves and non-analytical periodic cusp waves. Further, two-dimensional wave plots of analytical periodic solutions and non-analytical periodic cusp wave solutions are drawn to visualize the dynamics of the equation.展开更多
The travelling wave solutions of a generalized Camassa-Holm-Degasperis-Procesi equation ut-uxxt + (1 + b)umux = buxuxx + uuxxx are considered where b > 1 and m are positive integers. The qualitative analysis method...The travelling wave solutions of a generalized Camassa-Holm-Degasperis-Procesi equation ut-uxxt + (1 + b)umux = buxuxx + uuxxx are considered where b > 1 and m are positive integers. The qualitative analysis methods of planar autonomous systems yield its phase portraits. Its soliton wave solutions, kink or antikink wave solutions, peakon wave solutions, compacton wave solutions, periodic wave solutions and periodic cusp wave solutions are obtained. Some numerical simulations of these solutions are also given.展开更多
By constructing auxiliary differential equations, we obtain peaked solitary wave solutions of the generalized Camassa-Holm equation, including periodic cusp waves expressed in terms of elliptic functions.
By using modified simple equation method,we study the generalized RLW equation and symmetric RLW equation,the subsistence of solitary wave,periodic cusp wave,periodic bell wave solutions are obtained.We establish some...By using modified simple equation method,we study the generalized RLW equation and symmetric RLW equation,the subsistence of solitary wave,periodic cusp wave,periodic bell wave solutions are obtained.We establish some conditions on the parameters for which the obtained solutions are dark or bright soliton.The proficiency of the methods for constructing exact solutions has been established.Finally,the variety of structure and graphical representation makes the dynamics of the equations visible and provides the mathematical foundation in shallow water,plasma and ion acoustic plasma waves.展开更多
基金Supported by National Natural Science Foundation of China under Grant Nos.11361017,11161013Natural Science Foundation of Guangxi under Grant Nos.2012GXNSFAA053003,2013GXNSFAA019010Program for Innovative Research Team of Guilin University of Electronic Technology
文摘In this paper, we study peakon, cuspon, smooth soliton and periodic cusp wave of the generalized Schr6dinger-Boussinesq equations. Based on the method of dynamical systems, the generalized Schr6dinger-Boussinesq equations are shown to have new the parametric representations of peakon, cuspon, smooth solRon and periodic cusp wave solutions. Under different parametric conditions, various sufficient conditions to guarantee the existence of the above solutions are g/van.
文摘For the (2 + 1)-dimensional nonlinear dispersive Boussinesq equation, by using the bifurcation theory of planar dynamical systems to study its corresponding traveling wave system, the bifurcations and phase portraits of the regular system are obtained. Under different parametric conditions, various sufficient conditions to guarantee the existence of analytical and non-analytical solutions of the singular system are given by using singular traveling wave theory. For certain special cases, some explicit and exact parametric representations of traveling wave solutions are derived such as analytical periodic waves and non-analytical periodic cusp waves. Further, two-dimensional wave plots of analytical periodic solutions and non-analytical periodic cusp wave solutions are drawn to visualize the dynamics of the equation.
基金supported by China Postdoctoral Science Foundation (Grant Nos. 20100470249, 20100470254)
文摘The travelling wave solutions of a generalized Camassa-Holm-Degasperis-Procesi equation ut-uxxt + (1 + b)umux = buxuxx + uuxxx are considered where b > 1 and m are positive integers. The qualitative analysis methods of planar autonomous systems yield its phase portraits. Its soliton wave solutions, kink or antikink wave solutions, peakon wave solutions, compacton wave solutions, periodic wave solutions and periodic cusp wave solutions are obtained. Some numerical simulations of these solutions are also given.
基金Supported by the Nature Science Foundation of Shandong (No. 2004zx16,Q2005A01)
文摘By constructing auxiliary differential equations, we obtain peaked solitary wave solutions of the generalized Camassa-Holm equation, including periodic cusp waves expressed in terms of elliptic functions.
文摘By using modified simple equation method,we study the generalized RLW equation and symmetric RLW equation,the subsistence of solitary wave,periodic cusp wave,periodic bell wave solutions are obtained.We establish some conditions on the parameters for which the obtained solutions are dark or bright soliton.The proficiency of the methods for constructing exact solutions has been established.Finally,the variety of structure and graphical representation makes the dynamics of the equations visible and provides the mathematical foundation in shallow water,plasma and ion acoustic plasma waves.
