An Efficient Algorithm of Logarithmic Transformation to Hirota Bilinear Form of KdV-type Bilinear Equation

TL;DR

This paper presents a new, efficient algorithm for transforming KdV-type equations into Hirota bilinear form using logarithmic transformation, improving upon previous methods especially in coefficient determination.

Contribution

The paper introduces a novel algorithm leveraging properties of Hirota operators and logarithmic transformations to efficiently derive Hirota bilinear forms of KdV-type equations.

Findings

Algorithm outperforms previous methods in efficiency.

Effective in handling various integro-differential equations.

Improves accuracy in coefficient calculation.

Abstract

In this paper, an efficient algorithm of logarithmic transformation to Hirota bilinear form of the KdV-type bilinear equation is established. In the algorithm, some properties of Hirota operator and logarithmic transformation are successfully applied, which helps to prove that the linear terms of the nonlinear partial differential equation play a crucial role in finding the Hirota bilinear form. Experimented with various integro-differential equations, our algorithm is proven to be more efficient than the algorithm referred by Zhou, Fu, and Li in getting the Hirota bilinear form, especially in achieving the coefficient of the logarithmic transformation.