Periodic and Solitary Wave Solutions for the One-Dimensional Cubic Nonlinear Schrödinger Model

Ion Bica; Ana Mucalica

doi:10.2478/auom-2022-0018

Abstract

Using a similar approach as Korteweg and de Vries, [19], we obtain periodic solutions expressed in terms of the Jacobi elliptic function cn, [3], for the self-focusing and defocusing one-dimensional cubic nonlinear Schrödinger equations. We will show that solitary wave solutions are recovered through a limiting process after the elliptic modulus of the Jacobi elliptic function cn that describes the periodic solutions for the self-focusing nonlinear Schrödinger model.

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Periodic and Solitary Wave Solutions for the One-Dimensional Cubic Nonlinear Schrödinger Model

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