1. Solitary Waves of the Two-Dimensional Camassa-Holm--Nonlinear Schr��dinger Equation
- Author
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Ward, C. B., Mylonas, I. K., Kevrekidis, P. G., and Frantzeskakis, D. J.
- Subjects
Nonlinear Sciences::Exactly Solvable and Integrable Systems ,Mathematics::Analysis of PDEs ,FOS: Physical sciences ,Pattern Formation and Solitons (nlin.PS) ,Nonlinear Sciences::Pattern Formation and Solitons - Abstract
In this work, we study solitary waves in a (2+1)-dimensional variant of the defocusing nonlinear Schr��dinger (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., 10 pages, 6 figures
- Published
- 2018
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