Variable separation solutions and interacting waves of a coupled system of the modified KdV and potential BLMP equations

The multilinear variable separation approach (MLVSA) is applied to a coupled modified Korteweg-de Vries and potential Boiti-Leon-Manna-Pempinelli equations, as a result, the potential fields uy and vy are exactly the universal quantity applicable to all multilinear variable separable systems. The generalized MLVSA is also applied, and it is found that uy (vy) is rightly the subtraction (addition) of two universal quantities with different parameters. Then interactions between periodic waves are discussed, for instance, the elastic interaction between two semi-periodic waves and non-elastic interaction between two periodic instantons. An attractive phenomenon is observed that a dromion moves along a semi-periodic wave.