Asymptotic line solitons for the (2+1)-dimensional Sawada-Kotera-Kadomtsev-Petviashvili equation

We investigate a classification of the asymptotic line-soliton solutions to the (2+1)-dimensional Sawada-Kotera-Kadomtsev-Petviashvili (SKKP) equation by the Wronskian determinant form. We first prove that the SKKP equation has a solution in the Wronskian determinant form of the tau-function. It is then found that each tau-function can be represented by a point in the completely non-negative Grassmannian, so that the asymptotic behavior of the tau-function can be demonstrated, and the asymptotic line-soliton solutions can be obtained. We also show that such solutions have N asymptotic line solitons as \(y \rightarrow \infty \) $y\to \infty$ and \(M-N\) $M-N$ asymptotic line solitons in the opposite direction. We analyze the asymptotic line solitons for the soliton interactions through several examples, and illustrate in detail the various asymptotic solitons contained in the \((M-N,N)\) $(M-N,N)$ -soliton solutions.