Integrable Multi-Component Hybrid Nonlinear Schrödinger Equations

Abstract

Presented is a set of integrable multi-component hybrid nonlinear Schrödinger (MCHNS) equations. Each multi-component equation is a superposition of the nonlinear Schrödinger (NS) equation and the derivative nonlinear Schrödinger (DNS)equation. For the MCHNS equations, the inverse scattering formulation is given. The gauge transformation relating 2-component hybrid nonlinear Schrödinger equation with the Manakov equation is explicitly shown. This also confirms that the former is integrable since the latter is integrable.