Painlevé integrability, auto-Bäcklund transformations, new abundant analytic solutions including multi-soliton solutions for time-dependent extended KdV8 equation in nonlinear physics

Abstract

In this paper, a new eighth-order (1+1)-dimensional time-dependent extended KdV equation has been developed. This considered equation is being found completely integrable by using the Painlevé analysis method. Moreover, three auto-Bäcklund transformations have been generated by truncating the Painlevé series at a constant level. These auto-Bäcklund transformations have been used to derive various analytic solution families for the newly developed equation. These solutions include the kink-antikink soliton, kink-soliton, antikink-soliton, periodic-soliton, complex kink-soliton and complex periodic-soliton solutions. Multi-soliton solutions including N-soliton solution, have been obtained by using the simplified Hirota’s method for the considered equation. All the results are being expressed graphically to signify the physical importance of the considered equation.