Abstract
Abstract
The goal of this study is to get analytical solutions to the Bogoyavlensky-Konopelchenko equation, which describes an interaction of a long-wavelength wave moving along the x-axis and a Riemann wave-form moving along the y-axis. The equation has been widely used in soliton theory, fluid dynamics, optics, biological systems, and differential geometry. It is a member of the Ablowitz-Kaup-Newell-Segur hierarchy of integrable systems. By exploiting the classical Lie symmetry approach, the equation is reduced to an ordinary differential equation. After solving the second similarity reduction, the authors derived a novel class of solutions for each case. Additionally, the derived solutions comprise some parameters, and various functions might be utilized to explore wave profiles like stationary, dark, and bright soliton, parabolic dark and bright soliton, and progressive nature. Solutions are compared with previous researches [18–25] to show novelty of results. Solutions can help with numerous applications in physics, such as fluid dynamics, plasma physics, and nonlinear optics.