Starting from the zero solution, the standard multi-soliton solution, the soliton-like solution, kink-shape solution and periodic solutions are obtained. It is found that the PT-symmetry DNLSII equation possesses abundant solution structures. Finally, starting from zero and non-zero solutions, the expressions of explicit solutions are given. Then, according to the constraints of PT symmetry, the conditions that the parameters of the solution need to meet are deduced, and the solution of the PT-symmetry DNLSII equation is obtained. Firstly, the recursive form of the n-th order solution of the general DNLSII equation is derived with the help of the Darboux transformation matrix. This article introduces the PT symmetric DNLSII equation studied in this article on the basis of the research significance and background. The study of analytical solutions to nonlinear equations is one of the important issues studied by mathematical physicists in recent years. For example, in 2013, Ablowitz and Musslimani proposed a nonlinear Schr \(\ddot$$ Some special non-local models have been proposed. Generally, ( x, t) is far away from \((x_0,t_0)\), so the two-point system, or Alice–Bob system, is a non-local system. Equivalently, the operator is required to satisfy the condition \(f^2=1\).
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