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

Ion Bica; Ana Mucalica

doi:10.2478/auom-2022-0018

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

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

Volume 30 (2022): Issue 2 (May 2022)

By: Ion Bica and Ana Mucalica

Open Access

|Jun 2022

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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Articles in this issue

DOI: https://doi.org/10.2478/auom-2022-0018 | Journal eISSN: 1844-0835 | Journal ISSN: 1224-1784

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Language: English

Page range: 45 - 62

Submitted on: Jul 23, 2021

Accepted on: Sep 25, 2021

Published on: Jun 2, 2022

Published by: Ovidius University of Constanta

In partnership with: Paradigm Publishing Services

Publication frequency: 3 issues per year

Keywords:

NLS,

surface gravity waves,

Related subjects:

© 2022 Ion Bica, Ana Mucalica, published by Ovidius University of Constanta
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 30 (2022): Issue 2 (May 2022)