Rational Solutions for Two Nonautonomous Lattice Korteweg–de Vries Type Equations

Abstract

Up to now, many works have been conducted to deal with the rational solutions for the autonomous discrete integrable systems, while there have been few works on the rational solutions to the nonautonomous discrete integrable systems. In this paper, we investigate two nonautonomous lattice Korteweg–de Vries type equations: nonautonomous lattice potential Korteweg–de Vries equation and nonautonomous lattice potential modified Korteweg–de Vries equation. By the bilinear method, we construct the rational solutions for the aforesaid equations. These solutions are presented in terms of the Casoratian. By setting special forms of the lattice parameters of the nonautonomous lattice potential Korteweg–de Vries equation, dynamical behaviors for the first two rational solutions of this equation are analyzed with graphical illustration.

Keywords

• nonautonomous lattice Korteweg–de Vries type equations
• Casoratian solutions
• rational solutions
• dynamics