Asymptotics for large time of global solutions to the generalized Kadomtsev-Petviashvili equation
type: Item
instance of: scholarly article
title: Asymptotics for large time of global solutions to the generalized Kadomtsev-Petviashvili equation
zbMATH Open document ID: 0936.35158
author: Nakao Hayashi
author: Pavel I. Naumkin
author: Jean-Claude Saut
published in: Communications in Mathematical Physics
publication date: 2000-05-09T00:00:00Z
review text: The authors study the large time asymptotic behavior of solutions to the generalized Kadomtsev-Petviashvili equations \[ u_t+u_{xxx}+\sigma \partial_x^{-1} u_{yy}= -(u^p)_x, (t,x,y)\in \mathbb{R}\times \mathbb{R}^2, \] \[ u(0,x,y) =u_0(x,y), (x,y)\in \mathbb{R}^2, \] where \(\sigma=1\) or \(\sigma=-1\). If \(\rho\geq 3\) is an integer and the initial data are sufficiently small, then the solution \(u\) satisfies the following estimates: \[ \|u(t)\|_\infty \leq C(1+|t|)^{-1} (log(2+|t|))^k, \|u_x (t)\|_\infty \leq C(1+|t|)^{-1} \] for all \(t\in \mathbb{R}\), where \(k=1\) if \(\rho=3\) and \(k=0\) if \(\rho \geq 4\).
Mathematics Subject Classification ID: 35Q53
Mathematics Subject Classification ID: 35B40
zbMATH DE Number: 1334917
zbMATH Keywords: generalized Kadomtsev-Petviashvili equation
zbMATH Keywords: asymptotic behavior
reviewed by: Temur Jangveladze
MaRDI profile type: Publication
full work available at URL: s002200050569
OpenAlex ID: W2072572683
DOI: 10.1007/S002200050569
description: scientific article; zbMATH DE number 1334917