Study of a new nonlinear Kaup-Newell equations by using nonlocal symmetry method

Abstract

An important research topic in mathematical physics is the construction of high-dimensional integrable systems. First, based on the method of constructing a high-dimensional integrable system proposed by Lou et al. in this paper, a new (2+1)-dimensional Kaup-Newell (KN) equations are derived through the conservation laws of the (1+1)-dimensional KN equations. Subsequently, we study for the first time the new (1+1)-dimensional KN equations using nonlocal symmetric methods and with the help of constructed closed systems. We then obtained exact solutions of the KN equations, both explicit and special function solution.