Abundant exact solutions of higher-order dispersion variable coefficient KdV equation

Abstract

In this article, various exact solutions of the fifth-order variable coefficient KdV equation with higher-order dispersion term are studied. Because of the complexity of the exact solution of the variable coefficient t, it has a certain influence on the tension waves at the fluid interface on the gravity surface. First, the bilinear KdV equation is derived by using the Hirota bilinear method, and four mixed solutions consisting of positive quartic function, quadratic function, exponential function, and hyperbolic function are constructed. Second, the linear superposition principle is used to obtain the resonance multisoliton solution, and two cases are taken as examples to illustrate the study of resonance multi soliton solution. In addition, 3D images and contour images are drawn by mathematical symbol calculation and appropriate parameters, and the process of tension fluctuation is vividly explained by physical phenomena. The results obtained greatly expand the exact solution of the KdV equation in the existing literature and enable us to understand nonlinear dynamical systems more deeply.