Integrability, Lax pair and solitary interactions of the non-isospectral (2+1)-dimensional Gardner system on directional surface waves with large spreading angles

The non-isospectral generalization of the celebrated (2+1)-dimensional Gardner system describes various nonlinear phenomena and the characteristics of oceanic waves, physical plasmas, solid-state materials, etc. This paper utilizes an extended Bell polynomial approach to analyze a large class of non-isospectral integrable systems systematically. We exert a concrete investigation on the integrability of the non-isospectral and variable-coefficient (2+1)-dimensional Gardner equation, which describes the directional surface waves with large spreading angles. We obtain the bilinear formalism, bilinear Bäcklund transformations, Lax pair and kink-type solitary interactions of the corresponding system. Moreover, with a periodic alternation on the system's coefficients, we graphically analyze the propagation and interaction between its non-isospectral solitary wave trains.