Kundu方程的非线性波分支

Bifurcation of Kink Waves in the Kundu Equation

用动力系统分支理论研究Kundu方程u_t=iu_(xx)+i(c_3|u|~2+c_5|u|~4)u+α|u|~2u_x+βu^2_x的分支,通过变换u(x,t)=e^(-iωt)e^(iψ(ξ))φ(ξ)和ξ=x-ct,ψ′(ξ)=(c/2)+((α+β)/4)φ~2(ξ),揭示了由φ(ξ)表示的两种扭波解,分别是低扭波和高扭波.研究还发现两种有趣的分支现象:低扭波可以由高扭波、对称孤立波、爆破波和反对称波分支出来,而高扭波解可以由椭圆式周期波和三角函数式周期波分支出来.

In this paper,the Kundu equation is studied using bifurcation theory of dynamical systems.By transforming,and,two nonlinear waves expressed by are obtained:tall-kink waves and low-kink waves.Two interesting bifurcation phenomena are revealed.One is that the low-kink waves can be bifurcated from four types of nonlinear waves:tall-kink waves,symmetric solitary waves,blow-up waves and anti-symmetric solitary waves.The other is that the tall-kink waves can be bifurcated from two kinds of periodic waves expressed by trigonometric function and elliptic function respectively.