Modulation theory for soliton resonance and Mach reflection-Reference-Cited by-同舟云学术

Modulation theory for soliton resonance and Mach reflection

Published:2022-03 Issue:2259 Volume:478 Page:
ISSN:1364-5021
Container-title:Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
language:en
Short-container-title:Proc. R. Soc. A.

Author:

Ryskamp Samuel J.¹^ORCID,Hoefer Mark A.¹^ORCID,Biondini Gino²^ORCID

Affiliation:

1. Department of Applied Mathematics, University of Colorado, Boulder, CO 80309, USA

2. Department of Mathematics and Department of Physics, State University of New York, Buffalo, NY 14260, USA

Abstract

Resonant Y-shaped soliton solutions to the Kadomtsev–Petviashvili II (KPII) equation are modelled as shock solutions to an infinite family of modulation conservation laws. The fully two-dimensional soliton modulation equations, valid in the zero dispersion limit of the KPII equation, are demonstrated to reduce to a one-dimensional system. In this same limit, the rapid transition from the larger Y soliton stem to the two smaller legs limits to a travelling discontinuity. This discontinuity is a multivalued, weak solution satisfying modified Rankine–Hugoniot jump conditions for the one-dimensional modulation equations. These results are applied to analytically describe the dynamics of the Mach reflection problem, V-shaped initial conditions that correspond to a soliton incident upon an inward oblique corner. Modulation theory results show excellent agreement with direct KPII numerical simulation.

Funder

NSF

Publisher

The Royal Society

Subject

General Physics and Astronomy,General Engineering,General Mathematics

Link

https://royalsocietypublishing.org/doi/pdf/10.1098/rspa.2021.0823

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