Study on generalized variable coefficient fifth-order KdV equation based
on higher order dispersion term

- Zhen Zhao,
- Jing Pang

## Abstract

Nonlinear partial differential equations with higher order dispersion
terms play an important role in dynamics research. In this paper, the
fifth order KdV equation with high order dispersion term is studied and
discussed. Firstly, the bilinear form of the fifth order KdV equation
with high order dispersion term is derived by Hirota bilinear form.
Then, the combined test function of the positive quartic function,
quadratic function, exponential function and the interaction solution of
the hyperbolic function of the fifth order KdV equation with variable
coefficients is constructed, and the resonance multi-soliton test
function of the equation is constructed by using the linear
superposition principle.By means of mathematical symbol calculation, the
interaction solution between high-order Lump solution and periodic cross
kink solution of the fifth order KdV equation with variable coefficients
and its resonance multi-solitons are solved.And by observing its
corresponding graph analysis of its physical phenomenon.