New abundant analytic solutions for generalized KdV6 equation with time-dependent variable coefficients using Painlevé analysis and auto-Bäcklund transformation

Abstract

This paper considers the generalized KdV6 equation with time-dependent variable coefficients. The integrability of the considered equation is being examined by the Painlevé analysis method. Further, an auto-Bäcklund transformation method has been adopted to obtain the analytic solutions. Using this technique, five novel families of analytic solutions in the form of rational, exponential, hyperbolic and trigonometric functions have been successfully found for the considered equation. New kink-antikink and periodic soliton solutions have been discovered using this method. The solutions are graphically depicted to show the physical significance of the problem under consideration.