Interactions of breathers and solitons of a generalized variable-coefficient Korteweg-de Vries-modified Korteweg-de Vries equation with symbolic computation

Under investigation in this paper is a generalized variable-coefficient Korteweg-de Vries-modified Korteweg-de Vries equation which describes certain atmospheric blocking phenomenon. Lax pair and infinitely many conservation laws are obtained. With the help of the Hirota method and symbolic computation, the one-, two- and three-soliton solutions are given. Besides, breather and double pole solutions are derived. Propagation characteristics and interactions of breathers and solitons are discussed analytically and graphically. Results also show that the soliton changes its type between depression and elevation periodically. Parabolic-like breather and double pole are depicted. Conditions of the depression and elevation solitons are also given.