Painlevé analysis, auto-Bäcklund transformations, bilinear forms and soliton solutions for a (2+1)-dimensional variable-coefficient modified dispersive water-wave system in fluid mechanics

In this paper, we investigate a (2+1)-dimensional variable-coefficient modified dispersive water-wave system in fluid mechanics. We prove the Painlevé integrability for that system via the Painlevé analysis. We find some auto-Bäcklund transformations for that system via the truncated Painlevé expansions. Bilinear forms and N-soliton solutions are constructed, where N is a positive integer. We discuss the inelastic interactions, elastic interactions and soliton resonances for the two solitons. We also graphically demonstrate that the velocities of the solitons are affected by the variable coefficient of that system.