(2+1)维广义Nizhnik-Novikov-Veselov方程的新周期波、局域激发之间的相互作用

在分离变量法所得(2 1)维广义Nizhnik-Novikov-Veselov方程广义解(包含2个任意函数)中引入符合条件的Jacobi椭圆函数以及Jacobi椭圆函数的组合,从而获得了该系统的一些新双周期解.研究了这些周期波之间的相互作用,发现其相互作用是非弹性的.考虑下述2种极限情况:Jacobi椭圆函数的模数部分取0或1,能获得一种称作半局域(在一个方向上是周期的,而在另一个方向上是局域)的新结构,它们之间的相互作用也是非弹性的;Jacobi椭圆函数的模数全部取1,则获得了一些新的局域激发结构(two-dromion solution),研究表明,这类局域激发之间相互作用后仍然是非弹性的.

New periodic wave solutions,localized excitations and their interaction for (2+1)-dimensional generalized Nizhnik-Novikov-Veselov equation

A class of new doubly periodic wave solutions for generalized Nizhnik-Novikov-Veselov equation are obtained by introducing appropriate Jacobi elliptic function,Weierstrass elliptic function and their combization in the general solution(contains two arbitrariness functions)given by means of multi-linear variable separation approach.The interaction properties of periodic waves are found to be inelastic.Then two types limit cases are considered.Firstly,by taking one of the moduli to be unity and the other zero,particular wave(called semi-localized) patterns is obtained,which is periodic in one direction,but localized in the other direction.The interaction properties of these structures are found to be inelastic.Secondly,if both moduli are tending to 1 as a limit,some novel localized excitations(two-dromion solution) are derived.The results show that the interaction between the two dromions are also inelastic.