Exact solutions for the Bogoyavlensky-Konopelchenko equation with variable coefficients with an efficient technique

Abstract

In this investigation, a different form of extended generalized G′G2-expansion technique with variable coefficient is proposed. The advantage of the extended generalized G′G2–expansion technique is that it can be used to solve nonlinear evolution equations with both constant and variable coefficients, whereas the basic G′G2 method can only be used with constant coefficients. The proposed technique is used to solve the Bogoyavlensky–Konopelchenko (BK) equation with variable coefficients, which depicts the interaction of a Riemann wave propagating along the y-axis and a long wave propagating along the x-axis in a fluid. Further, the BK equation with variable coefficients is applied for stratified internal waves, shallow-water waves, ion-acoustic waves, and water propagation in a liquid. The hyperbolic, trigonometric, and rational form solutions of the BK equation are dynamically represented as the annihilation of three-dimensional kink waves, multi-soliton waves, single solitons, and so on. Furthermore, the derived solutions of the considered equation, which comprise arbitrary functional parameters and other constant parameters, can be used to enhance the advanced behaviours of physical situations.

Keywords

• Shock waves
• Multi-soliton
• Extended G′G2 generalized-expansion approach