Similarity Transformations and Nonlocal Reduced Integrable Nonlinear Schrödinger Type Equations

Abstract

We present three reduced integrable hierarchies of nonlocal integrable nonlinear Schrödinger-type equations, starting from a given vector integrable hierarchy generated from a matrix Lie algebra of B type. The basic tool is the zero curvature formulation. Three similarity transformations are taken to keep the invariance of the involved zero curvature equations. The key is to formulate a matrix solution to a reduced stationary zero curvature equation such that the zero curvature formulation works for a reduced case.

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