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Variational principle for generalized unstable and modify unstable nonlinear Schrödinger dynamical equations and their optical soliton solutions

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Abstract

In this paper, we investigate two types of nonlinear Schrödinger equations (NLSE): the unstable NLSE and the modify unstable NLSE. These equations describe the time evolution of disturbances in unstable media. To solve the proposed equations, we employ the variational principle method that involves selecting trial functions based on the Jost function in different forms. Also, these ansatz functions should be continuous at all intervals and may contain single or two nontrivial variational parameters. After that, we use these trial functions to find the functional integral and Lagrangian of the system without any loss. Besides, we use the amplitude ansatz method to explore new soliton solutions. The obtained results include various solitons, such as bright soliton, dark soliton, bright–dark solitary wave solutions, rational dark-bright soliton solutions, and periodic solitary wave solutions. The results will be displayed through different types of graphs, including 2D, 3D, and contour plots, which effectively highlight their outcomes. These solutions have essential applications in the fields of applied science and engineering. Also, they are stable and analytical solutions. The offered techniques can be utilized to solve numerous nonlinear models in mathematical physics and various applied sciences fields.

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  1. Mathematics Department, Faculty of Science, Taibah University, Al-Madinah Al-Munawarah, Kingdom of Saudi Arabia

    Aly R. Seadawy & Bayan A. Alsaedi

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  1. Aly R. Seadawy
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Seadawy, A.R., Alsaedi, B.A. Variational principle for generalized unstable and modify unstable nonlinear Schrödinger dynamical equations and their optical soliton solutions. Opt Quant Electron 56, 844 (2024). https://doi.org/10.1007/s11082-024-06417-4

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