An integrable symmetric (2+1)-dimensional Lotka–Volterra equation and a family of its solutions

Abstract

A symmetric (2+1)-dimensional Lotka–Volterra equation is proposed. By means of a dependent variable transformation, the equation is firstly transformed into multilinear form and further decoupled into bilinear form by introducing auxiliary independent variables. A bilinear Backlund transformation is found and then the corresponding Lax pair is derived. Explicit solutions expressed in terms of pfaffian solutions of the bilinear form of the symmetric (2+1)-dimensional Lotka–Volterra equation are given. As a special case of the pfaffian solutions, we obtain soliton solutions and dromions.