Some generalized coupled nonlinear Schrödinger equations and conservation laws
Abstract
Based on zero-curvature equation, a series of new four-component nonlinear Schrödinger-type equations related to a matrix problem are proposed by using the polynomial expansion of the spectral parameter. As two special reductions, a generalized coupled nonlinear Schrödinger equation and a generalized coupled derivative nonlinear Schrödinger equation are obtained. And then, the infinite conservation laws for each of these four-component nonlinear Schrödinger-type equations are constructed with the aid of the Riccati-type equations.