---

Journal of Applied Nonlinear Dynamics 1(2) (2012) 125--140 | DOI:10.5890/JAND.2012.05.002

Manel Labidi $^{1}$, Houria Triki $^{2}$, E.V. Krishnan $^{3}$, Anjan Biswas $^{4}$

$^{1}$ Laboratory of Engineering Mathematics, Tunisia Polytechnic School, University of 7th November at Carthage, BP 743, La Marsa 2070, TUNISIA

$^{2}$ Radiation Physics Laboratory, Department of Physics, Badji Mokhtar University, 2300 Anaba, ALGERIA

$^{3}$ Department of Mathematics and Statistics, Sultan Qaboos University, P. O. Box 36, Al Khod 123, Muscat, OMAN

$^{4}$ Department of Mathematical Sciences, Delaware State University, Dover, DE 19901-2277, USA

Download Full Text PDF

 

Abstract

This paper studies the generalized long-short wave equation with power law nonlinearity. There are several approaches that are used to solve this coupled system nonlinear evolution equations. The series solution approach yields the topological 1-soliton solution or shock wave solution. The ansatz method and the semiinverse variational principle leads to the non-topological 1-soliton of the equation. Additionally, the variational iteration method is used to study the equation. Finally, numerical simulations are also given to this equation.

References

1. [1]	Biswas, A. and Triki, H. (2010), 1-soliton solution of the Klein-Gordon-Schrödinger's equation with power law nonlinearity, Applied Mathematics and Computation, 217(8), 3869-3874.

2. [2]	Chowdhury, A. and Tataronis, J. (2008), Long wave-short wave resonance in nonlinear negative refractive index media, Physical Review Letters, 100, 153905.

3. [3]	Chang, Q., Wong, Y.-S., and Lin, C.-K. (2008), Numerical computations for long-wave short wave interaction equations in semi-classical limit, Journal of Computational Physics, 227(19), 8489-8507.

4. [4]	Coffey, M. W. (1990), On series expansions giving closed-form solutions of Korteweg-de Vries-like equations, SIAM Journal of Applied Mathematics, 50, 1580-1592.

5. [5]	Deng, C. and Shang, Y. (2009), Construction of exact periodic wave and solitary wave solutions for the long-short wave resonance equations by VIM, Communications in Nonlinear Science and Numerical Simulation, 14, 1186-1195.

6. [6]	Dong-long, L., Zheng-De L., and Yan-Feng, G. (2008), Periodic homoclinic wave of (1+1)-dimensional long-short wave equation, Chinese Physics Letters, 25(12), 4189-4191.

7. [7]	Ganji, S.S., Ganji, D.D., Sfahani, M.G., and Karimpour,S. (2010) , Application of AFF and HPM to the systems of strongly nonlinear oscillation, Current Applied Physics, 10(5), 1317-1325.

8. [8]	Hereman, W., Banerjee, P.P., Korpel, A., Assanto, G., Immerzeele, A. Van, and Meerpoel, A. (1986), Exact solitary wave solutions of non-linear evolution and wave equations using a direct algebraic method, Journal of Physics A, 19, 607-628.

9. [9]	Hongjun, G. and Guoguang, L. (1998), Attractor for weakly damped driven long wave-short wave resonance equation, Applied Mathematics, 13(4), 377-384.

10. [10]	Krishnan, E.V. (1995), Phase space analysis and the series method, Advances in Modeling and Analysis, 24, 53-63.

11. [11]	Krishnan E.V., and Biswas, A. (2010), Solutions of the Zakharov-Kuznetsov equation with higher order nonlinearity by mapping and ansatz method, Physics of Wave Phenomena, 18 (4), 256-261.

12. [12]	Labidi, M., and Omrani, K. (2011), Numerical simulation of the modified regularized long wave equation by He's variational iteration method, Numerical Methods for Partial Differential Equations, 27 (2), 478- 489.

13. [13]	Labidi, M., and Omrani, K. (2011), The use of variational iteration method and homotopy perturbation method for solving two nonlinear partial differential equations, International Journal of Numerical Methods for Heat and Fluid Flow, 21(4), 377-398.

14. [14]	Mehdipour, I., Ganji, D.D. and Mazaffari, M. (2010), Application of the energy balance method to nonlinear vibrating equations, Current Applied Physics, 10 (1), 104-112.

15. [15]	Shera, C.A., Tubis, A., and Talmadge, C.L. (2005), Coherent reflection in a two-dimensional cochlea: Short wave versus long wave scattering in the generalization of reflection-source otoacoustic emissions, Journal of the Acoustical Society of America, 118(1), 287-313.

16. [16]	Tatari, M., and Dehghan, M. (2009), Improvement of He's variational iteration method for solving systems of differential equations, Computers and Mathematics with Applications, 58, 2160-2166.

17. [17]	Ying-Hui, T., Han-Lin, C. and Xi-Qiang, L. (2006), New exact solutions to long-short wave interaction equations, Communications in Theoretical Physics, 46 (3), 397-402.

18. [18]	Yurova, M. (2007), Application of dressing method for long wave-short wave resonance interaction equation, Journal of Mathematical Physics, 48, 053516.

19. [19]	Wazwaz, A.M. (2007), The variational iteration method for solving linear and nonlinear systems of PDEs, Computers and Mathematics with Applications, 54, 895-902.

20. [20]	Wu, R., and Wang, W. (2009), Bifurcation and non-smooth dynamics of solitary waves in the generalized long-short wave equations, Applied Mathematical Modelling, 33(5) , 2218-2225.