Multi-Soliton Solutions for the Korteweg de Vries (KdV) Equation by Hirota Bilinear Method

Kang, Tien Wey (2023) Multi-Soliton Solutions for the Korteweg de Vries (KdV) Equation by Hirota Bilinear Method. Final Year Project (Bachelor), Tunku Abdul Rahman University of Management and Technology.

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Abstract

The Korteweg-de Vries (KdV) equation is a nonlinear partial differential equation used in mathematics and physics fields to describe shallowing water wave solutions There are two terms, nonlinear and dispersive in the KdV equation. These dispersive terms balance the nonlinear term's influence on newly formed solitons. The main goal of this project is to obtain multi-soliton solution of KdV equation. To create multi-soliton solutions to integrable nonlinear evolution equations, the Hirota bilinear method is applied. This method is a useful and direct way to search for N-soliton solutions to non-linear evolutionary equations compared with other methods. After obtaining the analytical result, the effect of changing the graph's parameters is observed and interpreted. The KdV equation's up to nine-soliton solutions will be demonstrated using MAPLE computer programming. Various properties of solitons such as behaviour, recurrence after collisions and phase shift were discussed. Keywords: Soliton, Hirota bilinear method, Korteweg de Vries equation