Conservation Laws in Higher-Order Nonlinear Optical Effects

Abstract

Conservation laws of the nonlinear Schrödinger equation are studied in the presence of higher-order nonlinear optical effects including the third-order dispersion and the self-steepening. In a context of group theory, we derive a general expression for infinitely many conserved currents and charges of the coupled higher-order nonlinear Schrödinger equation. The first few currents and charges are also presented explicitly. Due to the higher-order effects, conservation laws of the nonlinear Schrödinger equation are violated in general. The differences between the types of the conserved currents for the Hirota and the Sasa-Satsuma equations imply that the higher-order terms determine the inherent types of conserved quantities for each integrable cases of the higher-order nonlinear Schrödinger equation.

References in corpus (2)

• Matched Pulse Propagation in a Three-Level System
• Field Theory for Coherent Optical Pulse Propagation

Cited by in corpus (4)

• Painlevé analysis of the coupled nonlinear Schrödinger equation for polarized optical waves in an isotropic medium
• Rational W-shaped Optical Soliton on Continuous Wave in Presence of Kerr Dispersion and Stimulated Raman Scattering
• Anti-dark and Mexican-hat solitons in the Sasa-Satsuma equation on the continuous wave background
• High-order soliton solutions and their dynamics in the inhomogeneous variable coefficients Hirota equation