Abstract
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—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.
Highlights
The Korteweg-de Vries (KdV) equation, which is classic of all model equations of nonlinear waves in the soliton phenomena, is described
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; there is no significant effect to cause a change in their properties
In this paper we focus on the existence of more than one soliton solution called multi-solitons, since this enables us to study solitons collision or interactions especially for their said preserved behavior
Summary
The study of nonlinear evolution models which describes a large variety of physical phenomena is found to have two fascinating manifestations of opposite. A consequence of a dynamic balance between dispersion and nonlinear effects in any nonlinear evolution models. They are waves of permanent form that preserve their shape while traveling over long distances. The second implies that the wave has the property of a particle [1] [2] [3]
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