Stability Analysis for Travelling Wave Solutions of the Olver and Fifth-Order KdV Equations

Stability Analysis for Travelling Wave Solutions of the Olver and Fifth-Order KdV Equations

The Olver equation is governing a unidirectional model for describing long and small amplitude waves in shallow water waves. The solitary wave solutions of the Olver and fifth-order KdV equations can be obtained by using extended tanh and sech-tanh methods. The present results are describing the gen...

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Main Authors: A. R. Seadawy, W. Amer, A. Sayed
Format: Article
Language:English
Published: Hindawi Limited 2014-01-01
Series:Journal of Applied Mathematics
Online Access:http://dx.doi.org/10.1155/2014/839485
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spelling doaj-437ef820e6cc45d195611e6e82f2c49a2020-11-24T22:49:12ZengHindawi LimitedJournal of Applied Mathematics1110-757X1687-00422014-01-01201410.1155/2014/839485839485Stability Analysis for Travelling Wave Solutions of the Olver and Fifth-Order KdV EquationsA. R. Seadawy0W. Amer1A. Sayed2Mathematics Department, Faculty of Science, Taibah University, Al-Ula 41921-259, Saudi ArabiaMathematics Department, Faculty of Science, Taibah University, Al-Ula 41921-259, Saudi ArabiaMathematics Department, Faculty of Science, Beni-Suef University, Beni-Suef, EgyptThe Olver equation is governing a unidirectional model for describing long and small amplitude waves in shallow water waves. The solitary wave solutions of the Olver and fifth-order KdV equations can be obtained by using extended tanh and sech-tanh methods. The present results are describing the generation and evolution of such waves, their interactions, and their stability. Moreover, the methods can be applied to a wide class of nonlinear evolution equations. All solutions are exact and stable and have applications in physics.http://dx.doi.org/10.1155/2014/839485
collection DOAJ
language English
format Article
sources DOAJ
author A. R. Seadawy
W. Amer
A. Sayed
spellingShingle A. R. Seadawy
W. Amer
A. Sayed
Stability Analysis for Travelling Wave Solutions of the Olver and Fifth-Order KdV Equations
Journal of Applied Mathematics
author_facet A. R. Seadawy
W. Amer
A. Sayed
author_sort A. R. Seadawy
title Stability Analysis for Travelling Wave Solutions of the Olver and Fifth-Order KdV Equations
title_short Stability Analysis for Travelling Wave Solutions of the Olver and Fifth-Order KdV Equations
title_full Stability Analysis for Travelling Wave Solutions of the Olver and Fifth-Order KdV Equations
title_fullStr Stability Analysis for Travelling Wave Solutions of the Olver and Fifth-Order KdV Equations
title_full_unstemmed Stability Analysis for Travelling Wave Solutions of the Olver and Fifth-Order KdV Equations
title_sort stability analysis for travelling wave solutions of the olver and fifth-order kdv equations
publisher Hindawi Limited
series Journal of Applied Mathematics
issn 1110-757X
1687-0042
publishDate 2014-01-01
description The Olver equation is governing a unidirectional model for describing long and small amplitude waves in shallow water waves. The solitary wave solutions of the Olver and fifth-order KdV equations can be obtained by using extended tanh and sech-tanh methods. The present results are describing the generation and evolution of such waves, their interactions, and their stability. Moreover, the methods can be applied to a wide class of nonlinear evolution equations. All solutions are exact and stable and have applications in physics.
url http://dx.doi.org/10.1155/2014/839485
work_keys_str_mv AT arseadawy stabilityanalysisfortravellingwavesolutionsoftheolverandfifthorderkdvequations
AT wamer stabilityanalysisfortravellingwavesolutionsoftheolverandfifthorderkdvequations
AT asayed stabilityanalysisfortravellingwavesolutionsoftheolverandfifthorderkdvequations
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