Solitons for a (2+1)-dimensional variable-coefficient Bogoyavlensky-Konopelchenko equation in a fluid

In this letter, a (2+ 1)-dimensional variable-coefficient Bogoyavlensky-Konopelchenko equation is investigated, which describes the interaction of a Riemann wave propagating along the y-axis and a long wave propagating along the x-axis in a fluid. Under two different constraints of the time-dependent coefficients in this equation, two different bi-linear forms are derived by virtue of the binary Bell polynomials. Multiple solitary waves are constructed via the Hirota method, whose propagation properties and interaction characteristics are investigated graphically as well. Propagation and interaction of the solitons are illustrated graphically: (i) time-dependent coefficients affect the shape of the solitons; (ii) interaction of the solitons is elastic, i.e., amplitude, velocity and shape of each soliton remain invariant after each interaction except for a phase shift.