Analytical and Numerical Computations of Multi-Solitons in the Korteweg-de Vries (KdV) Equation

• 作者: Emem Ayankop-Andi Godwin J. Ibeh Hycienth O. Orapine
• 来源期刊: 应用数学(英文)
• 学科: 数学
• 关键词: Korteweg-de Vries Equation SOLITONS Hirota Method Crank-Nicolson Method
• 年，卷（期）: 2020,（7）
• 页码范围: 511-531
• 页数: 21页
• 分类号: O17

摘要

In this paper, an analytical and numerical computation of multi-solitons in Korteweg-de Vries (KdV) equation is presented. The KdV equation, which is classic of all model equations of nonlinear waves in the soliton phenomena, is described. In the analytical computation, the multi-solitons in KdV equation are computed symbolically using computer symbolic manipulator<span style="white-space:nowrap;">&#8212;</span>Wolfram Mathematica via Hirota method because of the lengthy algebraic computation in the method. For the numerical computation, Crank-Nicolson implicit scheme is used to obtain numerical algorithm for the KdV equation. The simulations of solitons in MATLAB as well as results concerning collision or interactions between solitons are presented. Comparing the analytical and numerical solutions, it is observed that the results are identically equal with little ripples in solitons after a collision in the numerical simulations;however there is no significant effect to cause a change in their properties. This supports the existence of solitons solutions and the theoretical assertion that solitons indeed collide with one another and come out without change of properties or identities.