The interactions of \(N\)-soliton solutions for the generalized (2+1)-dimensional variable-coefficient fifth-order KdV equation (Q277750)

Summary: A generalized (2+1)-dimensional variable-coefficient KdV equation is introduced, which can describe the interaction between a water wave and gravity-capillary waves better than the (1+1)-dimensional KdV equation. The \(N\)-soliton solutions of the (2+1)-dimensional variable-coefficient fifth-order KdV equation are obtained via the Bell-polynomial method. Then the soliton fusion, fission, and the pursuing collision are analyzed depending on the influence of the coefficient \(e^{A_{i j}}\); when \(e^{A_{i j}} = 0\), the soliton fusion and fission will happen; when \(e^{A_{i j}} \neq 0\), the pursuing collision will occur. Moreover, the Bäcklund transformation of the equation is gotten according to the binary Bell-polynomial and the period wave solutions are given by applying the Riemann theta function method.