A note on the wave propagation in water of variable depth

Demı́ray, Hilmi

doi:10.1016/j.amc.2011.07.049

Cited by 1 publication

(1 citation statement)

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“…A modified version of the KdV equation with the variable-depth is studied in Ref [3]. Some derivations of the variable-depth KdV equation that allow a bottom profile are discussed in Ref [3] and [5]. Another approach, spectral and pseudo-spectral numerical schemes for the KdV equation are discussed in Ref.…”

Section: Introductionmentioning

confidence: 99%

Application of Generalized Integral Method (GIRM) to Numerical Evaluations of Soliton-to-Soliton and Soliton-to-Bottom Interactions

Tsedendorj

Isshiki²,

Ravsal

2015

ACM

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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.

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Section: Introductionmentioning

confidence: 99%