Application of Generalized Integral Method (GIRM) to Numerical Evaluations of Soliton-to-Soliton and Soliton-to-Bottom Interactions
Applied and Computational Mathematics
Volume 4, Issue 3-1, June 2015, Pages: 78-86
Received: Apr. 17, 2015; Accepted: Apr. 17, 2015; Published: May 12, 2015
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Authors
Gantulga Tsedendorj, Department of Mathematics, National University of Mongolia, Ulaanbaatar, Mongolia
Hiroshi Isshiki, IMA, Institute of Mathematical Analysis, Osaka, Japan
Rinchinbazar Ravsal, Department of Administration, National University of Mongolia, Ulaanbaatar, Mongolia
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Abstract
Numerical evaluations of soliton-soliton and soliton-to-bottom interaction have many applications in various fields. On the other hand, Generalized Integral Representation Method (GIRM) is known as a convenient numerical method for solving Initial and Boundary Value Problem of differential equations such as advective diffusion. In this work, we apply one-step GIRM to numerical evaluations of propagation of a single soliton, soliton-to-soliton interaction and soliton-to-bottom interaction. Firstly, in case of a single soliton, the bottom is considered to be constant in order to understand the behavior of the soliton propagation as it travels in the middle of the sea. Next, in case of soliton-to-bottom, we study behavior of a single soliton propagation when the bottom has different geometries. Finally, we evaluate interaction of two different i.e., big and small solitons. To carry out with the studies, we derive and implement GIRM to numerically solve the Korteweg-de Vries (KdV) equation. In order to verify the theory, numerical experiments are conducted and accurate approximate solutions are obtained in each case of the soliton interactions.
Keywords
Korteweg-de Vries (KdV) equation, Single Soliton, Soliton-to-Soliton interaction, Soliton-to-Bottom interaction, Numerical Evaluation, Generalized Integral Representation Method (GIRM)
To cite this article
Gantulga Tsedendorj, Hiroshi Isshiki, Rinchinbazar Ravsal, Application of Generalized Integral Method (GIRM) to Numerical Evaluations of Soliton-to-Soliton and Soliton-to-Bottom Interactions, Applied and Computational Mathematics. Special Issue: Integral Representation Method and its Generalization. Vol. 4, No. 3-1, 2015, pp. 78-86. doi: 10.11648/j.acm.s.2015040301.16
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