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ANALYSIS OF $(1 + n)$ -DIMENSIONAL GENERALIZED CAMASSA–HOLM KADOMTSEV–PETVIASHVILI EQUATION THROUGH LIE SYMMETRIES, NONLINEAR SELF-ADJOINT CLASSIFICATION AND TRAVELLING WAVE SOLUTIONS

AMJAD HUSSAIN

https://orcid.org/0000-0002-5840-0846

Department of Mathematics, Quaid-I-Azam University, 45320 Islamabad, Pakistan

E-mail Address: a.hussain@qau.edu.pk

Corresponding author.

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ADIL JHANGEER

https://orcid.org/0000-0001-6747-425X

Department of Mathematics, Namal Institute, 30 Km Talagang Road, Mianwali 42250, Pakistan

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MUHAMMAD KHUBAIB ZIA

Department of Mathematics, Quaid-I-Azam University, 45320 Islamabad, Pakistan

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ILYAS KHAN

https://orcid.org/0000-0002-2056-9371

Department of Mathematics, College of Science Al-Zulfi, Majmaah University, Al-Majmaah, P. O. Box 66, Majmaah 11952, Saudi Arabia

E-mail Address: i.said@mu.edu.sa

Corresponding author.

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ABDUL HAMID GANIE

https://orcid.org/0000-0002-1787-5036

Basic Sciences Department, College of Science and Theoretical Studies, Saudi Electronic University-Abha, Male 61421, Saudi Arabia

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, and

SAYED M. ELDIN

Center of Research, Faculty of Engineering, Future University in Egypt, New Cairo 11835, Egypt

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https://doi.org/10.1142/S0218348X23400789Cited by:5 (Source: Crossref)

This article is part of the issue:

Special Issue on Fractal AI-Based Analyses and Applications to Complex Systems IV
Guest Editors: Yeliz Karaca, Dumitru Baleanu, Majaz Moonis, Yu-Dong Zhang and Osvaldo Gervasi

Abstract

In this paper, the nonlinear $(1 + n)$ -dimensional generalized Camassa–Holm Kadomtsev–Petviashvili (g-CH-KP) equation is examined using Lie theory. Lie point symmetries of the equation are computed using MAPLE software and are generalized for the case of any dimension. Moreover, the equation is transformed into a nonlinear ordinary differential equation using the Abelian subalgebra. The nonlinear self-adjoint classification of the equation under consideration is accomplished with the help of which conservation laws for a particular dimension are calculated. Moreover, the new extended algebraic approach is used to compute a wide range of solitonic structures using different set of parameters. Graphic description of some specific applicable solutions for certain physical parameters is portrayed.

Keywords:

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Vol. 31, No. 10

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History

Received 12 November 2021

Accepted 19 January 2023

Published: September 29, 2023

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This is an Open Access article in the “Special Issue on Fractal AI-Based Analyses and Applications to Complex Systems: Part IV”, edited by Yeliz Karaca https://orcid.org/0000-0001-8725-6719 (University of Massachusetts Chan Medical School, USA), Dumitru Baleanu https://orcid.org/0000-0002-0286-7244 (Cankaya University, Turkey & Institute of Space Sciences, Romania), Majaz Moonis https://orcid.org/0000-0002-9747-0003 (University of Massachusetts Chan Medical School, USA), Yu-Dong Zhang https://orcid.org/0000-0002-4870-1493 (University of Leicester, Leicester, UK) & Osvaldo Gervasi https://orcid.org/0000-0003-4327-520X (Perugia University, Perugia, Italy) published by World Scientific Publishing Company. It is distributed under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 (CC BY-NC-ND) License which permits use, distribution and reproduction, provided that the original work is properly cited, the use is non-commercial and no modifications or adaptations are made.

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