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arXiv · 1805.09837

Solitary Waves of the Two-Dimensional Camassa-Holm--Nonlinear Schr\"odinger Equation

C. B. Ward·I. K. Mylonas·P. G. Kevrekidis·D. J. Frantzeskakis
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Abstract

In this work, we study solitary waves in a (2+1)-dimensional variant of the defocusing nonlinear Schr\"odinger (NLS) equation, the so-called Camassa-Holm NLS (CH-NLS) equation. We use asymptotic multiscale expansion methods to reduce this model to a Kadomtsev--Petviashvili (KP) equation. The KP model includes both the KP-I and KP-II versions, which possess line and lump soliton solutions. Using KP solitons, we construct approximate solitary wave solutions on top of the stable continuous-wave solution of the original CH-NLS model, which are found to be of both the dark and anti-dark type. We also use direct numerical simulations to investigate the validity of the approximate solutions, study their evolution, as well as their head-on collisions.

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C. B. Ward, I. K. Mylonas, P. G. Kevrekidis, D. J. Frantzeskakis. 2018-05-24. Solitary Waves of the Two-Dimensional Camassa-Holm--Nonlinear Schr\"odinger Equation. https://doi.org/10.1088/1751-8121%2Faae7a2

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