Collapse for the Higher-order Nonlinear Schrödinger Equation

Authors

V. Achilleos, University of Athens
S. Diamantidis, University of the Aegean
D. J. Frantzeskakis, University of Athens
T. P. Horikis, University of Ioannina
N. I. Karachalios, University of the Aegean
P. G. Kevrekidis, University of Massachusetts Amherst

Publication Date

2016

Journal or Book Title

Physica D

Abstract

We examine conditions for finite-time collapse of the solutions of the higher-order nonlinear Schrödinger (NLS) equation incorporating third-order dispersion, self-steepening, linear and nonlinear gain and loss, and Raman scattering; this is a system that appears in many physical contexts as a more realistic generalization of the integrable NLS. By using energy arguments, it is found that the collapse dynamics is chiefly controlled by the linear/nonlinear gain/loss strengths. We identify a critical value of the linear gain, separating the possible decay of solutions to the trivial zero-state, from collapse. The numerical simulations, performed for a wide class of initial data, are found to be in very good agreement with the analytical results, and reveal long-time stability properties of localized solutions. The role of the higher-order effects to the transient dynamics is also revealed in these simulations.

Comments

Arxiv preprint uploaded. doi:10.1016/j.physd.2015.11.005

Pages

57-68

Volume

316

Recommended Citation

Achilleos, V.; Diamantidis, S.; Frantzeskakis, D. J.; Horikis, T. P.; Karachalios, N. I.; and Kevrekidis, P. G., "Collapse for the Higher-order Nonlinear Schrödinger Equation" (2016). Physica D. 1230.
Retrieved from https://scholarworks.umass.edu/math_faculty_pubs/1230