<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>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.</p>
</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.

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

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

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...

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

Published Online: Jun 02, 2022

Page range: 45 - 62

Received: Jul 23, 2021

Accepted: Sep 25, 2021

DOI: https://doi.org/10.2478/auom-2022-0018

Keywords
NLS, self-focusing, defocusing, dispersive, nonlinearity, carrier waves, solution profile, envelope, cnoidal waves, solitary waves, surface gravity waves, sound waves, water-air interface, sonic layer depth

© 2022 Ion Bica et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

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

Published Online: Jun 02, 2022

Page range: 45 - 62

Received: Jul 23, 2021

Accepted: Sep 25, 2021

DOI: https://doi.org/10.2478/auom-2022-0018

KeywordsNLS, self-focusing, defocusing, dispersive, nonlinearity, carrier waves, solution profile, envelope, cnoidal waves, solitary waves, surface gravity waves, sound waves, water-air interface, sonic layer depth

© 2022 Ion Bica et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
NLS, self-focusing, defocusing, dispersive, nonlinearity, carrier waves, solution profile, envelope, cnoidal waves, solitary waves, surface gravity waves, sound waves, water-air interface, sonic layer depth