Solutions to the fifth-order KP II equation scatter

被引：0
|
作者：
Perry, Peter A. [1 ]
Schuetz, Camille [2 ]
机构：
[1] Univ Kentucky, Dept Math, Lexington, KY 40506 USA
[2] Univ Wisconsin, Dept Math, Platteville, WI 53818 USA
来源：
NONLINEARITY | 2025年 / 38卷 / 04期
关键词：
nonlinear dispersive equations; scattering theory; long-time asymptotics; NONLINEAR SCHRODINGER-EQUATION; WELL-POSEDNESS; CAUCHY-PROBLEM;
D O I：
10.1088/1361-6544/adbcf1
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The fifth-order KP II equation describes dispersive long waves in two space dimensions. In this paper we show that solutions with small initial data scatter to solutions of the associated linear fifth-order equation. In particular, we establish the existence of nonlinear wave operators mapping the initial data to scattering asymptotes, and show that the nonlinear wave operators have inverses in a neighborhood of the origin. Our paper uses techniques developed for the third-order KP II equation by Hadac, Herr, and Koch.
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页数：28
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