Interactions Between Solitons and Cnoidal Periodic Waves of the (2+1)-Dimensional Konopelchenko—Dubrovsky Equation

Abstract

The (2+1)-dimensional Konopelchenko—Dubrovsky equation is an important prototypic model in nonlinear physics, which can be applied to many fields. Various nonlinear excitations of the (2+1)-dimensional Konopelchenko—Dubrovsky equation have been found by many methods. However, it is very difficult to find interaction solutions among different types of nonlinear excitations. In this paper, with the help of the Riccati equation, the (2+1)-dimensional Konopelchenko—Dubrovsky equation is solved by the consistent Riccati expansion (CRE). Furthermore, we obtain the soliton-cnoidal wave interaction solution of the (2+1)-dimensional Konopelchenko—Dubrovsky equation.