New analytical solutions and integrability for the (2 + 1)-dimensional variable coefficients generalized Nizhnik-Novikov-Veselov system arising in the study of fluid dynamics via auto-Backlund transformation approach

Abstract Recognising the non-uniformity of boundaries and the inhomogeneities of media, nonlinear evolution equations with variable coefficients may display more realistic scenarios dealing with time-varying environments and inhomogeneous media. In this work, the (2 + 1)-dimensional variable coefficients generalized Nizhnik-Novikov-Veselov system that occurs in the domain of fluid dynamics is investigated. Painlevé analysis technique is used to demonstrate the integrability of the above mentioned system. The governing equations are revealed to be integrable in the Painlevé sense under no specific criterion on the variable-coefficients. To derive numerous analytical solutions, the auto-Bäcklund transformation (ABT) method is taken into account. Consequently, three different analytical solutions are found using the ABT technique, which include linear, exponential, rational, and complex solutions. All the solutions are displayed as 3D plots in which variable coefficients and parameters are varied to produce the desired results. These graphs depict the many aspects of the proposed coupled system in the various forms of periodic waves and complex periodic wave surfaces.

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