Abstract
Abstract Analytical solutions of both the nonlinear Schrödinger equation (NLSE) and NLSE with a perturbation term have been attained. Besides, analytical solutions of nonlocal NLSE have also been obtained. In this paper, the nonlocal NLSE with a perturbation term is discussed. By virtue of the dependent variable substitution, trilinear forms of this equation is attained. Lax pairs and Darboux transformation of this equation are obtained. Via the Darboux transformation, two kinds solutions of this equation with the different seed solutions are attained.
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