Modified KdV equation with higher order dispersion terms

Abstract:

We consider the Cauchy problem for the modified Korteweg–de Vries equation with higher order dispersion terms ut-?xu3-?j=1n?j?x2j+1u=0,where ?j? R, n? 2. Our purpose in this paper is to prove the large time asymptoitic behavior of solutions under the non zero mass condition ? u(x) dx? 0. © 2019, Springer Nature Switzerland AG.

Keywords: Modified KdV Equation; Higher Order; Large Time Asymptotics Critical Nonlinearity; Self-Similar Solutions

MSC: 35Q53 (35B33 35B40 35C06)

Journal: NoDEA Nonlinear Differential Equations and Applications

ISSN: 1420-9004

Year: 2020

Volume: 27

Number: 1

Pages: 1

MR Number: 4037476

Revision: 1

URL: https://link.springer.com/article/10.1007%2Fs00030-019-0604-4

DOI: 10.1007%2Fs00030-019-0604-4