On the hyperbolic simulations to the Camassa-Holm equation
Електронний науковий архів Науково-технічної бібліотеки Національного університету "Львівська політехніка"
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
On the hyperbolic simulations to the Camassa-Holm equation
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| Creator |
Haci Mehmet Baskonus
Tukur Abdulkadir Sulaiman |
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| Contributor |
Munzur University
Firat University |
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| Subject |
The sine-Gordon expansion method
the Camassa-Holm equation complex function solution hyperbolic function solution trigonometric function solution |
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| Description |
In this paper, we apply the sine-Gordon expansion method to the Camassa-Holm equation. We obtain some new travelling wave solutions such as complex, hyperbolic and trigonometric function solutions. All the travelling wave solutions are verified by using Wolfram Mathematica 9 and they are indeed solutions to the model. We also plot the two- and three-dimensional surfaces for all the travelling wave solutions obtained in this paper using the same computer program.
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| Date |
2018-04-11T13:51:37Z
2018-04-11T13:51:37Z 2016 |
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| Type |
Conference Abstract
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| Identifier |
Haci Mehmet Baskonus On the hyperbolic simulations to the Camassa-Holm equation / Haci Mehmet Baskonus, Tukur Abdulkadir Sulaiman // Litteris et Artibus : proceedings of the 6th International youth science forum, November 24–26, 2016, Lviv, Ukraine / Lviv Polytechnic National University. – Lviv : Lviv Polytechnic Publishing House, 2016. – P. 97–100. – Bibliography: 18 titles.
http://ena.lp.edu.ua:8080/handle/ntb/40263 |
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| Language |
en
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| Relation |
[1] H.M. Baskonus and H. Bulut, “Exponential prototype structures for (2+1)-dimensional Boiti-Leon-Pempinelli systems in mathematical physics”, Waves in Random and Complex Media. 9 pages, 2016. [2] H.M. Baskonus, H. Bulut and F.M. Belgacem, “Analytical Solutions for Nonlinear Long-Short Wave Interaction Systems with Highly Complex Structure”, Journal of Computational and Applied Mathematics, 15 pages 2016. [3] E.M.E. Zayed, “Traveling wave solutions for higher dimensional nonlinlear evolution equations using the (G’/G)-expansion method”, Journal of Applied Mathematics Informatics. 28, 383-395, 2010. [4] M.A. Noor, K.I. Noor, A. Waheed and E.A. Al-Said, “Some new solitonary solutions of the modified Benjamin-Bona-Mahony equation”, Computer and Mathematics with Applications, 62, 2126-2131, 2011. [5] H. Bulut, H.M. Baskonus and S. Tuluce, “The Solution of Wave Equations by Sumudu Transform Method”, Journal of Advanced Research in Applied Mathematics. 4(3), 66-72, 2012. [6] A.M. Wazwaz and M.S. Mehanna, “A Variety of Exact TravellingWave Solutions for the (2+1)-Dimensional Boiti-Leon-Pempinelli Equation”, Appl. Math. Comput, 217, 1484-1490, 2010. [7] M. Najafi, S. Arbabi and M. Najafi, “He's Semi-Inverse Method for Camassa-Holm Equation and Simplified Modified Camassa-Holm Equation”, International Journal of Physical Research. 1(1), 1-6, 2013. [8] R. Camassa and D. Holm, “An Integrable Shallow Water Equation with Peaked Solitons”, Phys. Rev. Lett. 71(11), 1661-1664, 1993. [9] J. Boyd, “Traveling Wave Solutions of the Camassa-Holm Equation”, Appl. Math. Comput. 81(23), 73-87, 1997. [10] A. Bressan, “Global Dissipative Solutions of the Camassa-Holm Equation, Analysis and Applications. 5(1), 1-27, 2007. [11] H. Holden and X. Raynaud, “A Convergent Numerical Scheme for the Camassa-Holm Equation Based on Multipeakons”, Discrete and Contnuous Dynamical Systems. 14(3), 505-523, 2006. [12] R.S. Johnson, “On Solutions of the Camassa-Holm Equation”, Proc. R. Soc. Lond. 459, 1687-1708, 2003. [13] R.I. Ivanov, “Equations of the Camassa-Holm Hierarchy”, Theoretical and Mathematical Physics. 160(1), 952-959, 2009. [14] E.G. Reyes, “The Soliton Content of the Camassa-Holm and Hunter-Saxton Equations”, Proceedings of Institute of Mathematics of NAS of Ukraine. 43(1), 201-208, 2002. [15] C. Yan, “A Simple Transformation for Nonlinear Waves”, Physics Letters A, 22(4), 77-84, 1996. [16] H.M. Baskonus, “New Acoustic Wave Behaviors to the Davey-StewartsonEquation with Power Nonlinearity Arising in Fluid Dynamics”, Nonlinear Dynamics, 86(1), 177-183, 2016. [17] Z. Yan and H. Zhang, “New Explicit and exact Travelling Wave Solutionsfor a System of Variant Boussinesq equations in Mathematical Physics”, Physics Letters A, 252, 291-296, 1999. [18] [.W. Weisstein, “Concise Encyclopedia of Mathematics”, 2nd edition. NewYork: CRC Press, 2002.
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| Format |
97-100
application/pdf |
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| Coverage |
UA
Lviv |
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| Publisher |
Lviv Polytechnic Publishing House
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