Dynamical structures of interaction wave solutions for the two extended higher-order KdV equations

Abstract

In this paper, we investigate two extended higher-order KdV models (i.e., the extended Sawada–Kotera equation and the extended Lax equation), which can successfully describe propagation of dimly nonlinear long waves in fluids and ion-acoustic waves in harmonic sparklers. First, we present a general formula of multisoliton solutions of the two models. We then build the interaction solutions in terms of hyperbolic and sinusoidal functions by using multisoliton solutions with appropriate complex conjugate parameters controlling the phase shifts, propagation direction and energies of the waves. In particular, we present their collision solutions in the identical plane with different parametric constraints, which degenerate to the line rogue waves, x-shaped rogue waves, cnoidal periodic waves, interactions of rogue and bell waves, line breather and double breather waves. The dynamical characteristics of the wave solutions are shown graphically by choosing some special parameter values.