一个(3+1)维孤子方程的共振孤波解

The Resonant Soliton Wave Solutions of a (3+1) Dimensional Soliton Equation

基于双线性算子及其性质,结合孤子方程指数型传播波的线性叠加原理,讨论了一个(3+1)维非线性发展方程的孤波解,当M-波变元为实数时,将波的频率和数目参数化,构造出该孤子方程的扭状孤波和钟型孤波.将线性叠加原理推广到复数域来构造高维孤子方程的共振孤子解,这种复指数波函数解是由一系列指数和三角型波组合而成的M-波共振孤子解,随着时间的变化,这种多重孤波会产生共振现象.基于多重共振孤波解,在解空间中构造出该高维孤子方程的complexiton解.

On the basis of the bilinear operators and its properties, the soliton wave solutions for a(3+1)-dimensional nonlinear evolution equation were discussed in combination with the linear superposition principle of exponential traveling wave for soliton equations. When M-wave variables were real numbers, the kink-shape traveling wave and a bell-shape soliton of the soliton equation were presented by parameterizatian for wave frequencies and wave numbers. The resonant soliton solutions of high dimensional soliton equations were obtained by extending the linear superposition principle to complex field, this kind of the complex exponential wave function solutions were M-wave resonant soliton solutions composed of a series of exponential and trigonometric waves. The resonant phenomena of multiple soliton waves were occured with the development of time. Based on the resonant multiple soliton wave solutions, the complexiton solutions of the high-dimensional soliton equation were obtained in the space of solutions.