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arXiv · 2106.05413

Solitary waves with intensity-dependent dispersion: variational characterization

D. E. Pelinovsky·R. M. Ross·P. G. Kevrekidis
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Abstract

A continuous family of singular solitary waves exists in a prototypical system with intensity-dependent dispersion. The family has a cusped soliton as the limiting lowest energy state and is formed by the solitary waves with bell-shaped heads of different lengths. We show that this family can be obtained variationally by minimization of mass at fixed energy and fixed length of the bell-shaped head. We develop a weak formulation for the singular solitary waves and prove that they are stable under perturbations which do not change the length of the bell-shaped head. Numerical simulations confirm the stability of the singular solitary waves.

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D. E. Pelinovsky, R. M. Ross, P. G. Kevrekidis. 2021-06-09. Solitary waves with intensity-dependent dispersion: variational characterization. https://doi.org/10.1088/1751-8121%2Fac284f

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