Application of tanh–coth method for combined and double combined sinh–cosh–Gordon equations arising from chemical reactions to water surface gravity waves

Akhmetshin, Elvir; Abdullayev, Ilyos; Makhmudov, Samariddin; Dakhkilgova, Kamila; Korotaeva, Irina; Yanovskaya, Galina

doi:10.22034/cmde.2025.67655.3234

Application of tanh–coth method for combined and double combined sinh–cosh–Gordon equations arising from chemical reactions to water surface gravity waves

Document Type : Research Paper

Authors

¹ 1. Department of Economics, Mamun University, Khiva, Uzbekistan. \\ 2. Faculty of Economics, RUDN University, Moscow, Russia.

² Department of Business and Management, Urgench State University, Urgench, Uzbekistan.

³ 1. Department of Finance and Tourism, Termez University of Economics and Service, Termez, Uzbekistan.\\ 2. Department of Finance, Alfraganus University, Tashkent, Uzbekistan.

⁴ Department of programming and infocommunication technologies, Kadyrov Chechen State University, Grozny, Russia.

⁵ Department I-11 Foreign language for aerospace specialties, Moscow Aviation Institute, Moscow, Russia.

10.22034/cmde.2025.67655.3234

Abstract

An application of the generalized tanh–coth method to search for exact solutions of nonlinear partial differential equations is analyzed. This method is used for the combined and the double combined sinh-cosh-Gordon equations. The generalized tanh–coth method was used to construct periodic wave and solitary wave solutions of nonlinear evolution equations. This method is developed for searching for exact travelling wave solutions of nonlinear partial differential equations. It is shown that the generalized $tanh-coth$ method, with the help of symbolic computation, provides a straightforward and powerful mathematical tool for solving nonlinear problems.

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