It has been found that some nonlinear wave equations have one-loop soliton solutions. What is the dynamical behavior of the so-called one-loop soliton solution? To answer this question, the travelling wave solutions for four nonlinear wave equations are discussed. Exact explicit parametric representations of some special travelling wave solutions are given. The results of this paper show that a loop solution consists of three different breaking travelling wave solutions. It is not one real loop soliton travelling wave solution.
Ji-bin LI Department of Mathematics, Zhejiang Normal University, Jinhua 321004, China
Chaotic behavior for the two-component Bose-Einstein condensate system is considered.Under given parameter con...
Jibin Li1,2 (1Department of Mathematics,Zhejiang Normal University,Jinhua,Zhejiang,321004,P.R.China and 2Kunming University of Science and Technology Kunming,Yunnan,650093,P.R.China)
By using the method of dynamical systems to the two-component generalization of the Camassa-Holm equation, the existence of solitary wave solutions, kink and anti-kink wave solutions, and uncountably infinite many breaking wave solutions, smooth and non-smooth periodic wave solutions is obtained. Under different parametric conditions, various sufficient conditions to guarantee the existence of the above solutions are given. Some exact explicit parametric representations of travelling wave solutions are listed.
By finding a parabola solution connecting two equilibrium points of a planar dynamical system, the existence of the kink wave solution for 6 classes of nonlinear wave equations is shown. Some exact explicit parametric representations of kink wave solutions are given. Explicit parameter conditions to guarantee the existence of kink wave solutions are determined.
This paper considers the problems of determining center or focus and isochronous centers for the planar quasi-analytic systems. Two recursive formulas to determine the focal values and period constants are given. The convergence of first integral near the center is proved. Using the general results to quasi-quadratic systems, the problem of the isochronous center of the origin is completely solved.
The exact parametric representations of the traveling wave solutions for a nonlinear elastic rod equation are considered. By using the method of planar dynamical systems, in different parameter regions, the phase portraits of the corresponding traveling wave system are given. Exact explicit kink wave solutions, periodic wave solutions and some unbounded wave solutions are obtained.
