D.E. Pelinovsky, R.M. Ross, and P.G. Kevrekidis

Solitary waves with intensity-dependent dispersion: variational characterization

J. Phys. A: Math. Theor. 54 (2021) 445701 (15 pages)

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.

Keywords:
nonlinear Schrodinger equation, intensity-dependent dispersion, solitary waves, variational characterization, Lyapunov stability