SOLITARY WAVE EVOLUTION FOR MKDV EQUATIONS

摘要: The evolution of an initial condition into soliton(s) is the classic problem for Korteweg-de Vries (KdV) equation. While this theoretically given by inverse scattering solution KdV equation, in practice only final steady state can be easily obtained from scattering. However, approximate method based on conservation laws equation has been found to give very accurately soliton( s) . This also gives a criterion number solitons formed. In present work, extended describe solitary wave(s) mKdV equations, these equations having same dispersive term as but nonlinear form U”U x, where n 2 1 positive integer. It that < 4, behaviour similar evolve arbitrary condition. it sufficiently small amplitude decays radiation with no wave being For exceeding threshold, blows-up. solutions are compared full numerical and good agreement found.