KdV-type Wronskian rational solutions to the (4+1)-dimensional Fokas equation

Abstract

The purpose of this paper is to discuss the (4+1)-dimensional Fokas equation, which has been investigated as an integrable generalization of the KP equation and the DS equation. A general Wronskian structure is set up and the involved functions for Wronskian entries satisfy a system of combined linear partial differential equations, based on the Wronskian conditions of the KdV equation. The resulting Wronskian formulation gives a comprehensive way to build rational solutions for the (4+1)-dimensional Fokas equation. Moreover, the linear superposition principle for two Wronskian rational solutions is also obtained by employing a polynomial identity. The presented results show that the exact solutions of the (4+1)-dimensional Fokas equation can be reduced to the exact solutions of the KdV equation.

Keywords

• The Fokas equation
• Wronskian
• Rational solutions
• Linear superposition