Solutions to the fifth-order KP II equation scatter

Peter A. Perry; Camille Schuetz

doi:10.1088/1361-6544/adbcf1

Solutions to the fifth-order KP II equation scatter

Peter A. Perry, Camille Schuetz

Mathematics

Research output: Contribution to journal › Article › peer-review

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	https://doi.org/10.1088/1361-6544/adbcf1
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.

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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10.1088/1361-6544/adbcf1

Cite this

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AB - 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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JO - Nonlinearity

JF - Nonlinearity

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Solutions to the fifth-order KP II equation scatter

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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