Final state problem for class of nonlinear nonlocal dispersive equation

[摘要] We study the large time asymptotics of the solutions to nonlinear dispersive equations of the form partial derivative(t)u - P(-i partial derivative(x))partial derivative(x)u = -partial derivative(x)(u(3)), t > 0, x is an element of R, (0.1) where P(-i partial derivative(x)) is a pseudo-differential operator defined by the symbol P(xi). In this paper, we consider the case that P(xi) is nonlocal and nonhomogeneous and show the existence of the solution to (0.1) around a given modified free solution. (C) 2019 Elsevier Inc. All rights reserved.

[发布日期] 2019-12-15

[关键词] Nonlocal dispersive equation;Smith equation;Intermediate long-wave equation;Large time asymptotics