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Изучается долговременна́я асимптотика нелокального уравнения Кунду типа нелинейного уравнения Шредингера с убывающими начальными данными, полученная на основе метода нелинейного наискорейшего спуска, предложенного Дейфтом и Чжоу, и метода Римана-Гильберта.

The generalized mixed nonlinear Schrödinger equation is the core of this thesis study and it plays a pivotal position in many physical applications. In this paper, on the whole, in the framework of the Riemann–Hilbert approach, by analyzing the spectral problem of the Lax pair and applying the transformation of the matrix, the Riemann–Hilbert problem of the generalized mixed nonlinear Schrödinger equation for specific values of the parameters is constructed. After that, in the case of irregularity, the [Formula: see text]-soliton solutions of this equation at specific values of the parameters can be presented by the scattering transformation. In particular, some three-dimensional images of this nonlinear system can be graphically depicted.

In this paper, we study the [Formula: see text]-soliton solutions for the Hirota and Maxwell–Bloch equation with physical meaning. From the Lax pair and Volterra integral equations, the Riemann–Hilbert problem of this integrable equation is constructed. By solving the matrix Riemann–Hilbert problem with the condition of no reflecting, the [Formula: see text]-soliton solutions for the Hirota and Maxwell–Bloch equation are obtained explicitly. Finally, we simulate the three-dimensional diagram of [Formula: see text] with 2-soliton solutions and the motion trajectory of [Formula: see text]-axis in the case of different [Formula: see text].