# Spacial inhomogeneity and nonlinear tunneling for the forced KdV equation

## TL;DR

This paper studies a variable-coefficient forced KdV equation with spatial inhomogeneity, deriving multi-soliton solutions, analyzing inhomogeneity effects, and exploring nonlinear tunneling phenomena relevant to fluids and plasmas.

## Contribution

It introduces a method to transform the inhomogeneous equation into bilinear form and derives multi-soliton solutions, highlighting the effects of spatial inhomogeneity and nonlinear tunneling.

## Key findings

- Inhomogeneity affects soliton velocity, width, and background.
- Nonlinear tunneling can amplify or compress soliton amplitude.
- Results are applicable to fluid and plasma physics.

## Abstract

A variable-coefficient forced Korteweg-de Vries equation with spacial inhomogeneity is investigated in this paper. Under constraints, this equation is transformed into its bilinear form, and multi-soliton solutions are derived. Effects of spacial inhomogeneity for soliton velocity, width and background are discussed. Nonlinear tunneling for this equation is presented, where the soliton amplitude can be amplified or compressed. Our results might be useful for the relevant problems in fluids and plasmas.