Analytic localized solitonic excitations for the (2+1)-dimensional variable-coefficient breaking soliton model in fluids and plasmas

In this paper, via the Painlevé analysis and multi-linear variable separation, the (2 + 1)- dimensional variable-coefficient breaking soliton model in certain fluids and plasmas is investigated, with the Bäcklund transformation and analytic solutions presented explicitly. With those solutions, four kinds of the localized solitonic excitations are obtained, as the multi-shock-lump, multi-instanton, saddle-type-multiple-ring-soliton, and single-loopbreather structures. Figures indicate that the shapes, velocities, and propagation paths of those four kinds are affected by the variable coefficients, yielding the dynamic features, elastic interactions, parallel propagations, and periodic propagation of the analytic bound localized solitonic excitations.