Shallow water wave models with and without singular kernel: existence, uniqueness, and similarities
type: Item
instance of: scholarly article
title: Shallow water wave models with and without singular kernel: existence, uniqueness, and similarities
zbMATH Open document ID: 1426.35223
DOI: 10.1155/2017/4609834
author: E. F. Doungmo Goufo
author: Sunil Kumar
published in: Mathematical Problems in Engineering
publication date: 2018-11-05T00:00:00Z
review text: Summary: After the recent introduction of the Caputo-Fabrizio derivative by authors of the same names, the question was raised about an eventual comparison with the old version, namely, the Caputo derivative. Unlike Caputo derivative, the newly introduced Caputo-Fabrizio derivative has no singular kernel and the concern was about the real impact of this nonsingularity on real life nonlinear phenomena like those found in shallow water waves. In this paper, a nonlinear Sawada-Kotera equation, suitable in describing the behavior of shallow water waves, is comprehensively analyzed with both types of derivative. In the investigations, various fixed-point theories are exploited together with the concept of Piccard \(\mathcal{K} \)-stability. We are then able to obtain the existence and uniqueness results for the models with both versions of derivatives. We conclude the analysis by performing some numerical approximations with both derivatives and graphical simulations being presented for some values of the derivative order \(\gamma \). Similar behaviors are pointed out and they concur with the expected multisoliton solutions well known for the Sawada-Kotera equation. This great observation means either of both derivatives is suitable to describe the motion of shallow water waves.
Mathematics Subject Classification ID: 35R11
Mathematics Subject Classification ID: 35Q53
Mathematics Subject Classification ID: 76B15
zbMATH DE Number: 6972117
describes a project that uses: GTEngine
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2017/4609834
OpenAlex ID: W2586827336
Wikidata QID: Q59147558
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description: scientific article; zbMATH DE number 6972117