Infinite conservation laws and new solutions of (3+1)-dimensional generalized Konopelchenko–Dubrovsky–Kaup–Kupershmidt equation

In this paper, a (3+1)-dimensional generalized Konopelchenko–Dubrovsky–Kaup–Kupershmidt equation (gKDKK) is investigated. Based on Bell polynomial theory, the bilinear form, Bilinear Bäcklund transformation, Lax pair and infinite conservation laws of the equation are obtained. Lump solution and half periodic kink solution are obtained by combining the test function with bilinear form. Furthermore, with the help of the variable separation method, we obtain some new compound solutions composed of exponential function, trigonometric function, hyperbolic function, rational function and Jacobi elliptic function in various forms. Using computer software to draw the three-dimensional diagram and profile of the solutions, the dynamic properties of the solutions are analyzed.