The coupled modified nonlinear Schrödinger equations are under investigation in this work. Starting from analyzing the spectral problem of the Lax pair, a Riemann-Hilbert problem for the coupled modified nonlinear Schrödinger equations is formulated. And then, through solving the obtained Riemann-Hilbert problem under the conditions of irregularity and reflectionless case, N-soliton solutions for the equations are presented. Furthermore, the localized structures and dynamic behaviors of the one-soliton solution are shown graphically.

We aim to construct multi-soliton solutions for the coupled Fokas–Lenells system which arises as a model for describing the nonlinear pulse propagation in optical fibers. Starting from the spectral analysis of the Lax pair, a Riemann–Hilbert problem is presented. Then in the framework of the Riemann–Hilbert problem corresponding to the reflectionless case, N-soliton solutions to the coupled Fokas–Lenells system are derived explicitly.

This paper studies the N-soliton solutions of the generalized nonlinear Schrödinger equation. Firstly, the spectral analysis of a Lax pair is carried out. Secondly, the Riemann–Hilbert (RH) problem is established. Finally, the RH problem without reflection is considered and the expression of general N-soliton solutions of the equation is obtained.

In this paper, we use the Hirota bilinear method to find the [Formula: see text]-soliton solution of a [Formula: see text]-dimensional generalized Kadovtsev–Petviashvili (KP) equation. Then, we obtain the [Formula: see text]-order breathers of the equation, and combine the long-wave limit method to give the [Formula: see text]-order lumps. Resorting to the extended homoclinic test technique, we obtain the breather-kink solutions for the equation. Last, the interaction solution composed of the [Formula: see text]-soliton solution, [Formula: see text]-breathers, and [Formula: see text]-lumps for the [Formula: see text]-dimensional generalized KP equation is constructed.

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