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.