Exact solutions of unsteady Korteweg-de Vries and time regularized long wave equations

In this paper, we implement the exp(−Φ(ξ))-expansion method to construct the exact traveling wave solutions for nonlinear evolution equations (NLEEs). Here we consider two model equations, namely the Korteweg-de Vries (KdV) equation and the time regularized long wave (TRLW) equation. These equations...

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Detalles Bibliográficos
Autores principales: Islam, S M Rayhanul, Khan, Kamruzzaman, Akbar, M Ali
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2015
Materias:
Research
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4368646/
https://www.ncbi.nlm.nih.gov/pubmed/25810953
http://dx.doi.org/10.1186/s40064-015-0893-y
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author Islam, S M Rayhanul
Khan, Kamruzzaman
Akbar, M Ali
author_facet Islam, S M Rayhanul
Khan, Kamruzzaman
Akbar, M Ali
author_sort Islam, S M Rayhanul
collection PubMed
description In this paper, we implement the exp(−Φ(ξ))-expansion method to construct the exact traveling wave solutions for nonlinear evolution equations (NLEEs). Here we consider two model equations, namely the Korteweg-de Vries (KdV) equation and the time regularized long wave (TRLW) equation. These equations play significant role in nonlinear sciences. We obtained four types of explicit function solutions, namely hyperbolic, trigonometric, exponential and rational function solutions of the variables in the considered equations. It has shown that the applied method is quite efficient and is practically well suited for the aforementioned problems and so for the other NLEEs those arise in mathematical physics and engineering fields. PACS numbers: 02.30.Jr, 02.70.Wz, 05.45.Yv, 94.05.Fq.
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spelling pubmed-43686462015-03-25 Exact solutions of unsteady Korteweg-de Vries and time regularized long wave equations Islam, S M Rayhanul Khan, Kamruzzaman Akbar, M Ali Springerplus Research In this paper, we implement the exp(−Φ(ξ))-expansion method to construct the exact traveling wave solutions for nonlinear evolution equations (NLEEs). Here we consider two model equations, namely the Korteweg-de Vries (KdV) equation and the time regularized long wave (TRLW) equation. These equations play significant role in nonlinear sciences. We obtained four types of explicit function solutions, namely hyperbolic, trigonometric, exponential and rational function solutions of the variables in the considered equations. It has shown that the applied method is quite efficient and is practically well suited for the aforementioned problems and so for the other NLEEs those arise in mathematical physics and engineering fields. PACS numbers: 02.30.Jr, 02.70.Wz, 05.45.Yv, 94.05.Fq. Springer International Publishing 2015-03-12 /pmc/articles/PMC4368646/ /pubmed/25810953 http://dx.doi.org/10.1186/s40064-015-0893-y Text en © Islam et al.; licensee Springer. 2015 This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly credited.
spellingShingle Research
Islam, S M Rayhanul
Khan, Kamruzzaman
Akbar, M Ali
Exact solutions of unsteady Korteweg-de Vries and time regularized long wave equations
title Exact solutions of unsteady Korteweg-de Vries and time regularized long wave equations
title_full Exact solutions of unsteady Korteweg-de Vries and time regularized long wave equations
title_fullStr Exact solutions of unsteady Korteweg-de Vries and time regularized long wave equations
title_full_unstemmed Exact solutions of unsteady Korteweg-de Vries and time regularized long wave equations
title_short Exact solutions of unsteady Korteweg-de Vries and time regularized long wave equations
title_sort exact solutions of unsteady korteweg-de vries and time regularized long wave equations
topic Research
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4368646/
https://www.ncbi.nlm.nih.gov/pubmed/25810953
http://dx.doi.org/10.1186/s40064-015-0893-y
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