Travelling wave solutions to nonlinear Schrodinger equation with self-steepening and self-frequency shift

TL;DR

This paper derives exact traveling wave solutions for a higher order nonlinear Schrödinger equation with self-steepening and self-frequency shift, revealing diverse soliton behaviors including superluminal, subluminal, bright, and dark solitons with chirality.

Contribution

It introduces new exact localized solutions to a modified nonlinear Schrödinger equation accounting for higher order effects and self-phase modulation, expanding understanding of soliton dynamics in femtosecond regimes.

Findings

Existence of both superluminal and subluminal solitons with chirality.

Bright and dark solitons in different dispersion regimes.

Dark solitons propagate with non-zero velocity, unlike in nanosecond regimes.

Abstract

We investigate exact travelling wave solutions of higher order nonlinear Schrodinger equation in the absence of third order dispersion, which exhibit non-trivial self phase modulation. It is shown that, the corresponding dynamical equation, governing the evolution of intensity in the femtosecond regime, is that of non-linear Schrodinger equation with a source. The exact localized solutions to this system can have both super and subluminal propagation belonging to two distinct class. A number of these solitons exhibit chirality, thereby showing preferential propagation behavior determined by group velocity dispersion. Both localized bright and dark solitons are found in complementary velocity and experimental parameter domains, which can exist for anomalous and normal dispersion regimes. It is found that, dark solitons in this system propagate with non-zero velocity, unlike their counterpart in nanosecond regime. Interestingly, subluminal propagation is observed for solitons having a nontrivial Pade type intensity profile.