Integrability with symbolic computation on the Bogoyavlensky–Konoplechenko model: Bell-polynomial manipulation, bilinear representation, and Wronskian solution

Abstract

With symbolic computation, this paper investigates some integrable properties of a two-dimensional generalization of the Korteweg-de Vries equation, i.e., the Bogoyavlensky–Konoplechenko model, which can govern the interaction of a Riemann wave propagating along the \(y\)-axis and a long wave propagating along the \(x\)-axis. Within the framework of Bell-polynomial manipulations, Bell-polynomial expressions are firstly given, which then are cast into bilinear forms. The \(N\)-soliton solutions in the form of an \(N\)th-order polynomial in the \(N\) exponentials and in terms of the Wronskian determinant are, respectively, constructed with the Hirota bilinear method and Wronskian technique. Bilinear Backlund transformation is also derived with the achievement of a family of explicit solutions.