Abstract
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.
| Original language | English |
|---|---|
| Article number | 045011 |
| Journal | Nonlinearity |
| Volume | 38 |
| Issue number | 4 |
| DOIs | |
| State | Published - Apr 30 2025 |
Bibliographical note
Publisher Copyright:© 2025 IOP Publishing Ltd & London Mathematical Society. All rights, including for text and data mining, AI training, and similar technologies, are reserved.
Funding
The authors thank the referees for a number of useful comments which have improved our paper. Peter Perry acknowledges the support of the Simons Foundation for part of the time this work was done.
| Funders |
|---|
| Simons Foundation |
Keywords
- 35B40
- 35P25
- 35Q53
- 37L50
- long-time asymptotics
- nonlinear dispersive equations
- scattering theory
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics
- General Physics and Astronomy
- Applied Mathematics
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