Lump-soliton interaction solutions to differential-difference mKdV systems in (2+1)-dimensions

Lump-soliton interaction solutions to continuous integrable systems have been pretty well studied, but there are relatively few results in the differential-difference (DΔ) case. In this paper, some (2+1)-dimensional DΔ-mKdV systems are investigated by using Hirota's bilinear operator method. By setting appropriate variable transformations and assuming auxiliary functions as quadratic and exponential functions, lump-soliton interaction solutions are derived. Certain fission∖fusion phenomena of the physical quantity, the velocity of the potential, are explored by analyzing dynamical behaviors of the resultant solutions with different values of the involved parameters.