The qualitative theory of differential equations is applied to the Ostrovsky equation.The cusped solitonand loop-soliton solutions of the Ostrovsky equation are obtained.Asymptotic behavior of cusped soliton solutions...The qualitative theory of differential equations is applied to the Ostrovsky equation.The cusped solitonand loop-soliton solutions of the Ostrovsky equation are obtained.Asymptotic behavior of cusped soliton solutions isgiven.Numerical simulations are provided for cusped solitons and so-called loop-solitons of the Ostrovsky equation.展开更多
In this paper, the Lie symmetry analysis and generalized symmetry method are performed for a short-wave model. The symmetries for this equation are given, and the phase portraits of the traveling wave systems are anal...In this paper, the Lie symmetry analysis and generalized symmetry method are performed for a short-wave model. The symmetries for this equation are given, and the phase portraits of the traveling wave systems are analyzed using the bifurcation theory of dynamical systems. The exact parametric representations of four types of traveling wave solutions are obtained.展开更多
In this letter, we investigate traveling wave solutions of a nonlinear wave equation with degenerate dispersion. The phase portraits of corresponding traveling wave system are given under different parametric conditio...In this letter, we investigate traveling wave solutions of a nonlinear wave equation with degenerate dispersion. The phase portraits of corresponding traveling wave system are given under different parametric conditions. Some periodic wave and smooth solitary wave solutions of the equation are obtained. Moreover, we find some new hyperbolic function compactons instead of well-known trigonometric function compactons by analyzing nilpotent points.展开更多
基金Supported by the National Natural Science Foundation of China under Grant Nos.10961011 and 60964006
文摘The qualitative theory of differential equations is applied to the Ostrovsky equation.The cusped solitonand loop-soliton solutions of the Ostrovsky equation are obtained.Asymptotic behavior of cusped soliton solutions isgiven.Numerical simulations are provided for cusped solitons and so-called loop-solitons of the Ostrovsky equation.
基金Project supported by the Foundation of Guangxi Key Laboratory of Trusted Software, the Guangxi Natural Science Foundation, China (Grant No. 2011GXNSFA018134)the National Natural Science Foundation of China (Grant Nos. 11161013 and 61004101)
文摘In this paper, the Lie symmetry analysis and generalized symmetry method are performed for a short-wave model. The symmetries for this equation are given, and the phase portraits of the traveling wave systems are analyzed using the bifurcation theory of dynamical systems. The exact parametric representations of four types of traveling wave solutions are obtained.
基金Supported by the National Natural Science Foundation of China under Grant Nos.11161013,11361017,and 11301106Foundation of Guangxi Key Lab of Trusted Software and Program for Innovative Research Team of Guilin University of Electronic TechnologyProject of Outstanding Young Teachers’Training in Higher Education Institutions of Guangxi
文摘In this letter, we investigate traveling wave solutions of a nonlinear wave equation with degenerate dispersion. The phase portraits of corresponding traveling wave system are given under different parametric conditions. Some periodic wave and smooth solitary wave solutions of the equation are obtained. Moreover, we find some new hyperbolic function compactons instead of well-known trigonometric function compactons by analyzing nilpotent points.
