New extended Jacobi elliptic function expansion scheme for wave-wave interaction in ionic media
https://doi.org/10.17586/2220-8054-2018-9-5-581-585
Abstract
New Jacobi Elliptic functions expansion scheme, more general than the hyperbolic tangent function method, is derived to construct the exact wave solutions in terms of Jacobi Elliptic functions. The coupled 1D nonlinear Schrodinger–Zakharov (CNLSZ) system is taken as the model ¨ equation for wave-wave interaction in ionic media. It is shown that more new solutions can be obtained at their limit condition.
About the Authors
R. D. Pankaj
Department of Mathematics, J. N. V. University
India
India
Jodhpur
B. Singh
Department of Mathematics, J. N. V. University
India
India
Jodhpur
A. Kumar
2Department of Mathematics, Government College Kota
India
India
Kota (Raj.)
References
1. Langmuir I. Oscillations in Ionized Gases. Proc. Natl. Acad. Sci. U.S.A., 1928, 14 (8), P. 627–637.
2. Tonks L., Langmuir I. Oscillations in Ionized Gases. Physical Review, 1929, 33, P. 195–210.
3. Chen F.F. Introduction to Plasma Physics, Plenum, New York, 1974.
4. Scott C., Chu F.Y.F., Mcglaughlin D.W. The soliton: a new concept in applied science. Proc. IEEE, 1973, 61, P. 1443–1483.
5. Zakharov V.E. Collapse of Langmuir Waves. JEPT, 1972, 35 (5), P. 908–914.
6. Pereira N.R., Sudan R.N., Denavit J. ”Numerical study of two-dimensional generation and collapse of Langmuir solitons. The Physics of Fluids, 1977, 20 (6), P. 936–945.
7. Nicholson D.R., et al. Nonlinear Langmuir waves during type III solar radio bursts. The Astrophysical Journal, 1978, 223, P. 605–619.
8. Goldman M.V., Nicholson D.R. Virial theory of direct Langmuir collapse. Physical Review Letters, 1978, 41 (6), P. 406.
9. Nicholson R., Goldman M.V. Cascade and collapse of Langmuir waves in two dimensions. Phys. Fluids, 1978, 21 (10), P. 1766–1776.
10. Hasegawa A. Stimulated Modulational Instabilities of Plasma Waves. Phys. Rev. A, 1970, 1 (6), P. 1746.
11. Thyagaraja A. Recurrence, dimensionality, and Lagrange stability of solutions of the nonlinear Schrodinger equation. ¨ Phys. of Fluids, 1981, 24 (11), P. 1973–1975.
12. Russell D.A., Ott E. Chaotic (strange) and periodic behavior in instability saturation by the oscillating twostream instability. The Physics of Fluids, 1981, 24 (11), P. 1976–1988.
13. Weatherall J.C., et al. Solitons and ionospheric heating. Journal of Geophysical Research: Space Physics, 1982, 87 (A2), P. 823–832.
14. Vakhnenko V.O., Parkes E.J., Morrison A.J. A Backlund transformation and the inverse scattering transform method for the generalised Vakhnenko equation. Chaos, Solitons & Fractals, 2003, 17 (4), P. 683–692.
15. Ye-peng Sun, Jin-bo Bi, Deng-yuan Chen. N-soliton solutions and double Wronskian solution of the non-isospectral AKNS equation. Chaos, Solitons & Fractals, 2005, 26 (3), P. 905–912.
16. Sakka A. Backland transformations for Painleve I and II equations to Painleve-type equations of second order and higher degree. Phys. Lett. A, 2002, 300 (2–3), P. 228–232.
17. Yao R.X., Li Z.B. New exact solutions for three nonlinear evolution equations. Phys. Lett. A, 2002, 297, P. 196–204.
18. Kumar A. An analytical solution for a coupled partial differential equation. Applied Mathematics and Computation, 2009, 212, P. 245–250.
19. Liu Z., Chen C. Compactons in a general compressible hyper elastic rod. Chaos, Solitons & Fractals, 2004, 22 (3), P. 627–640.
20. Kaya D., El-Sayed S.M. An application of the decomposition method for the generalized KdV and RLW equations. Chaos, Solitons & Fractals, 2003, 17 (5), P. 869–877.
21. Hagtae Kim, Dong Pyo Hong, Kil to Chong. A numerical solution of point kinetics equations using the Adomian Decomposition Method. Systems and Informatics (ICSAI), 2012 International Conference on IEEE 19–20 May 2012, 12835470.
22. Kumar A., Ram D.P. Solitary Wave Solutions of Schrodinger Equation by Laplace–Adomian Decomposition Method. ¨ Physical Review & Research International, 2013, 3 (4), P. 702–712.
23. Ghoreishi M., Ismail A.I.B., Rashid A. Numerical Solution of Klein–Gordon–Zakharov Equations using Chebyshev Cardinal Functions. Journal of Computational Analysis & Applications, 2012, 14 (1), P. 574–582.
24. Zhao Xiaofei, Ziyi Li. Numerical Methods and Simulations for the Dynamics of One-Dimensional Zakharov-Rubenchik Equations. Journal of Scientific Computing, 2013, 59 (2), P. 412–438.
25. Kumar A., Ram D.P., Manish G. Finite difference scheme of a model for nonlinear wave-wave interaction in ionic media. Computational Mathematics and Modeling, 2011, 22 (3), P. 255–265.
26. Kumar A., Ram D.P. Finite Difference Scheme for the Zakharov Equation as a Model for Nonlinear Wave-Wave Interaction in Ionic Media. International Journal of Scientific & Engineering Research, 2014, 5 (2), P. 759–762.
27. Kumar A., Ram D.P. Solitary Wave Solutions of Schrodinger Equation by Laplace–Adomian Decomposition Method. ¨ Physical Review & Research International, 2013, 3 (4), P. 702–712.
Review
For citations:
Pankaj R.D., Singh B., Kumar A. New extended Jacobi elliptic function expansion scheme for wave-wave interaction in ionic media. Nanosystems: Physics, Chemistry, Mathematics. 2018;9(5):581-585. https://doi.org/10.17586/2220-8054-2018-9-5-581-585
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