Solitons and other exact solutions for two nonlinear PDEs in mathematical physics using the generalized projective Riccati equations method
type: Item
instance of: scholarly article
title: Solitons and other exact solutions for two nonlinear PDEs in mathematical physics using the generalized projective Riccati equations method
zbMATH Open document ID: 1404.35090
DOI: 10.1155/2018/6870310
author: A. M. Shahoot
author: K. A. E. Alurrfi
author: I. M. Hassan
author: A. M. Almsri
published in: Advances in Mathematical Physics
publication date: 2018-12-11T00:00:00Z
review text: Summary: We apply the generalized projective Riccati equations method with the aid of Maple software to construct many new soliton and periodic solutions with parameters for two higher-order nonlinear partial differential equations (PDEs), namely, the nonlinear Schrödinger (NLS) equation with fourth-order dispersion and dual power law nonlinearity and the nonlinear quantum Zakharov-Kuznetsov (QZK) equation. The obtained exact solutions include kink and antikink solitons, bell (bright) and antibell (dark) solitary wave solutions, and periodic solutions. The given nonlinear PDEs have been derived and can be reduced to nonlinear ordinary differential equations (ODEs) using a simple transformation. A comparison of our new results with the well-known results is made. Also, we drew some graphs of the exact solutions using Maple. The given method in this article is straightforward and concise, and it can also be applied to other nonlinear PDEs in mathematical physics.
Mathematics Subject Classification ID: 35C08
zbMATH DE Number: 6991998
zbMATH Keywords: nonlinear Schrödinger equation
zbMATH Keywords: nonlinear quantum Zakharov-Kuznetsov equation
zbMATH Keywords: kink and antikink solitons
describes a project that uses: Maple
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2018/6870310
OpenAlex ID: W2802595902
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Wikidata QID: Q129911333
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description: scientific article; zbMATH DE number 6991998