Trigonometric shock waves for the Kaup-Boussinesq system
Sergey K. Ivanov, Anatoly M. Kamchatnov
TL;DR
This paper introduces a new class of trigonometric shock wave solutions for the Kaup-Boussinesq system, expanding understanding of nonlinear wave propagation in physical systems with stable modulational behavior.
Contribution
It presents the discovery of trigonometric shock wave solutions within the Whitham modulation framework for the Kaup-Boussinesq system, a novel analytical development.
Findings
Analytical derivation of trigonometric shock wave solutions.
Numerical confirmation of the analytical results.
Identification of non-zero wave excitation in initial discontinuity evolution.
Abstract
We consider the modulationally stable version of the Kaup-Boussinesq system which models propagation of nonlinear waves in various physical systems. It is shown that the Whitham modulation equations for this model have a new type of solutions which describe trigonometric shock waves. In the Gurevich-Pitaevskii problem of evolution of an initial discontinuity, these solutions correspond to a non-zero wave excitation on one of the sides of the discontinuity. Our analytical results are confirmed by numerical calculations.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Mathematical Physics Problems · Nonlinear Waves and Solitons · Nonlinear Photonic Systems