Traveling waves of nonlinear Schrödinger equation including higher order dispersions

Abstract

The solitary wave solution and periodic solutions expressed in terms of elliptic Jacobi's functions are obtained for the nonlinear Schrödinger equation governing the propagation of pulses in optical fibers including the effects of second, third and fourth order dispersion. The approach is based on the reduction of the generalized nonlinear Schrödinger equation to an ordinary nonlinear differential equation. The periodic solutions obtained form one-parameter family which depend on an integration constant $p$. The solitary wave solution with ${\mathrm{sech}}^2$ shape is the limiting case of this family with $p=0$. The solutions obtained describe also a train of soliton-like pulses with ${\mathrm{sech}}^2$ shape. It is shown that the bounded solutions arise only for special domains of integration constant.

arXiv commentWe consider in this paper also the case with negative parameter $\gamma$ (defocusing nonlinearity)

References in corpus (6)

• Observation of Quantum Shock Waves Created with Ultra Compressed Slow Light Pulses in a Bose-Einstein Condensate
• Optical Solitary Waves in the Higher Order Nonlinear Schrodinger Equation
• On Dispersive and Classical Shock Waves in Bose-Einstein Condensates and Gas Dynamics
• Pure-Quartic Solitons
• Formation of Quantum Shock Waves by Merging and Splitting Bose-Einstein Condensates
• Solitary Waves in Optical Fibers Governed by Higher Order Dispersion

Cited by in corpus (3)

• Propagation of coupled quartic and dipole multi-solitons in optical fibers medium with higher-order dispersions
• Propagation of periodic and solitary waves in a highly dispersive cubic-quintic medium with self-frequency shift and self-steepening nonlinearity
• An existence theory for nonlinear equations on metric graphs via energy methods