Solitary and periodic wave solutions of the loaded Boussinesq and the loaded modified Boussinesq equation

Volume 30, Issue 1, pp 67--74 https://doi.org/10.22436/jmcs.030.01.07

Publication Date: December 01, 2022 Submission Date: April 30, 2022 Revision Date: September 22, 2022 Accteptance Date: October 07, 2022

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Authors

B. Babajanov - Department of Applied Mathematics and Mathematical Physics, Urgench State University, Urgench, Uzbekistan. F. Abdikarimov - Khorezm Mamun Academy, Khiva, Uzbekistan.

Abstract

In this article, we establish new traveling wave solutions for the loaded Boussinesq equation and the loaded modified Boussinesq equation by the functional variable method. The performance of this method is reliable and effective and gives the exact solitary wave solutions and periodic wave solutions of the loaded Boussinesq equation and its modifications. The traveling wave solutions obtained via this method are expressed by hyperbolic functions and the trigonometric functions. The graphical representations of some obtained solutions are demonstrated to better understand their physical features, including bell-shaped solitary wave solutions, singular soliton solutions and solitary wave solutions of kink type. This method presents a wider applicability for handling nonlinear wave equations.

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Keywords

• Loaded modified Boussinesq equation
• hyperbolic functions
• trigonometric functions
• periodic wave solutions
• soliton solutions
• functional variable method

MSC

•  34A34
•  34B15
•  35Q51
•  35J60
•  35J66

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