Research ArticleOpen AccessGoogle Scholar indexed
Numerical Estimation of Traveling Wave Solution of Two-Dimensional K-dV Equation Using a New Auxiliary Equation Method
Department of Mathematics, Jagannath University, Dhaka, Bangladesh
Department of Mathematics, BUET, Dhaka, Bangladesh
Department of Mathematics, Jahangirnagar University, Savar, Bangladesh
- 1 Department of Mathematics, Jagannath University, Dhaka, Bangladesh
- 2 Department of Mathematics, BUET, Dhaka, Bangladesh
- 3 Department of Mathematics, Jahangirnagar University, Savar, Bangladesh
American Journal of Computational Mathematics·Volume 03 (2013)·Pages 27–36·Published 26 March 2013·DOI10.4236/ajcm.2013.31004
Copy link · social · email
Abstract
Korteweg de-Vries (K-dV) has wide applications in physics, engineering and fluid mechanics. In this the Korteweg de- Vries equation with traveling solitary waves and numerical estimation of analytic solutions have been studied. We have found some exact traveling wave solutions with relevant physical parameters using new auxiliary equation method introduced by PANG, BIAN and CHAO. We have solved the set of exact traveling wave solution analytically. Some numerical results of time dependent wave solutions have been presented graphically and discussed. This procedure has a potential to be used in more complex system of many types of K-dV equation .
KeywordsContorPropagationSoliton PeriodicTime Evolution
- Yu. N. Zaiko, “Quasiperiodic Solutions of the Kortewegd Vries Equation,” Technical Physics Letters, Vol. 28. No. 3, 2002, pp. 235-236. doi:10.1134/1.1467286
- F. L. Qu and W. Q. Wang, “Alternating Segment Explicit—Implicit Scheme for Nonlinear Third-Order KdV Equation,” Applied Mathematics and Mechanics, Vol. 28, No. 7, 2007, pp. 973-980. doi:10.1007/s10483-007-0714-y
- N. E. Zhukovskii, “Hydraulic Shock in water Pipelines,” Gostekhteorizdal, Moscow, 1949.
- A. C. Newell, “Solitons in Mathematics and Physics,” SIAM, Philadelphia, 1985.
- V. A. Rukavishnikov and O. P. Tkachenko, “The Korteweg-de Vries Equation in a Cylindrical Pipe,” Computational Mathematics and Mathematical Physics, Vol. 48, No. 1, 2008, pp. 139-146. doi:10.1134/S0965542508010107
- N. Smaoui and R. H. Al-Jamal, “Boundary Control of the Generalized Korteweg-de Vries-Burgers Equation,” Nonlinear Dynamics, Vol. 51, 2008, pp. 439-446.
- J. Pang, C.-Q. Bian and L. Chao, “A New Auxiliary Equation Method for Finding Traveling Wave Solution to K-dV Equation,” Applied Mathematics and Mechanics (English Edition), Vol. 31, No. 7, 2010, pp. 929-936.
- L. Debnath, “Linear Partial Differential Equations for Scientists and Engineers,” 4th Edition, Tyn Myint-U, 2007, pp. 573-580.
- R. L. Herman, “Solitary Waves,” American Scientist, Vol. 80, 1992, pp. 350-361.
- P. A. Clarkson and M. D. Kruskal, “New Similarity Reductions of the Boussinesq Equation,” Journal of Mathematical Physics, Vol. 30, No. 10, 1989, pp. 2201-2213. doi:10.1063/1.528613