A New Composite Technique to Obtain Non-traveling Wave Solutions of the (2+1)-dimensional Extended Variable Coefficients Bogoyavlenskii–Kadomtsev–Petviashvili Equation

In this article, we investigate non-traveling wave solutions for the (2+1)-dimensional extended variable coefficients Bogoyavlenskii–Kadomtsev–Petviashvili equation with time-dependent (VC-BKP). Inspired by Shang $$^{[24]}$$ , apply three-wave method and generalized separation to investigated problem first time in article. The technique is effective, easily applicable, reliable solving solutions. We successfully obtain forty-four exact solutions, including double periodic kinky breather solution, cross-kink solution some new obtained firstly paper. These results all have a tail which gives prediction of physical phenomenon. Moreover, discuss arbitrary real, purely imaginary complex domains, greatly enriches forms dynamic phenomena four types are demonstrated contour, 2D 3D graphics, help show their interpretation.