Vol. 5 (04) pp. 1323-1330 DOI: 10.21474/IJAR01/3950

DEVELOPMENT OF MODULATIONAL INSTABILITIES IN TRAVELING WAVE SOLUTIONS FOR WAVE-WAVE INTERACTION IN IONIC MEDIA.

, and
  • Research Scholar, Department of Mathematics, Career Point University, Kota (Raj.), India.
  • Department of Mathematics, Government College Kota, Kota (Raj.), India.
  • Department of Mathematics, J.N.V. University, Kota (Raj.), India.
11 Downloads 99 Views
Crossref

Download Full Paper (PDF)

Abstract

In this paper, the development of modulational instabilities are shown in traveling wave solutions which are calculated using exp -expansion Method. These solutions completely new and have not found in earlier. But the solutions found in the Ref. [20] are the same to our obtain solutions. By means of this scheme, we found some new travelling wave solutions of the above mentioned equations. The exp(-Φ(ξ))- expansion method can be easily applied to solve the NLDEs and provides some new solutions. The solutions obtained in this article have been checked by putting them back into the original equation and found correct.

Article Analytics

References

  1. O. Rice, (1954) Mathematical analysis of random noise, in: N. Wax (Ed.), Noise and Stochastic Processes, Dover Publications, New York, pp. 133?294.
  2. S. Longuet-Higgins, (1952) On the statistical distribution of the heights of sea waves, J. Marine Res. 11 1245?1266.
  3. S. Longuet-Higgins, (1963) The effect of non-linearities on statistical distributions in the theory of sea waves, J. Fluid Mech. 17 459?480.
  4. A. Tayfun, (1980) Narrow?band nonlinear sea waves, J. Geophys. Res. 85 1548?1552.
  5. E. Zakharov. (1972). Collapse of Langmuir waves. Zh Eksp Teor Fiz, 62, 1745?1751.
  6. Mv Golman. (1986). Langmuir wave solitons and spatial collapse in plasma physics. Physica, D 18, P. 67?76.
  7. Michel Moisan, Jacques Pelletier. (2012): Hydrodynamic description of plasma, in: Physics of Collisional Plasmas, Springer. Netherlands.p. 203?335.
  8. H. Li. (1993). Langmuir turbulence equations with the self-generated magnetic field. Phys. Fluids, B 5, P. 350?356.
  9. Malomed, D. Anderson, M. Lisak, M.L. Quiroga-Teixeiro. (1977). Dynamics of solitary waves in the Zakharov model equations. Phys. Rev., E 55, P. 962?968.
  10. H. He. (2005).Application of homotopy perturbation method to nonlinear wave equations, Chaos Solitons Fract., 26 (3), P. 695?700.
  11. H. He, X.H. Wu. (2006). Construction of solitary solution and compaction-like solution by variational iteration method. Chaos Solitons Fract, 29 (1), P. 108?113.
  12. H. He. (1999). Variational iteration method ? a kind of nonlinear analytical technique: some examples. Int. J. Nonlinear Mech, 34 (4), P. 699?708.
  13. H. He. (2000). Variational iteration method for autonomous ordinary differential systems. Appl. Math. Comput., 114 (2?3), P. 115?123.
  14. M. Odibat, S. Momani. (2006). Application of variational iteration method to nonlinear differential equations of fractional order. Int. J. Nonlinear Sci. Numer. Simul., 7 (1) P. 27?36.
  15. Mehmet Giyas Sakar, Fevzi Erdogan, Ahmet Yıldırım. (2012). Variational iteration method for the time-fractional Fornberg? Whitham equation. Comput. Math. Appl., 63(9), P. 1382? 1388.
  16. H. He, Guo-Cheng Wu, F. Austin. (2010). The variational iteration method which should be followed. Nonlinear Sci. Lett. A?Math. Phys. Mech., 1 (1), P. 1?30.
  17. Arun Kumar. (2005). A variational method to study the Zakharov equation. Int. J. Math. Math. Sci., 22, P. 3703?3709.
  18. Kaya, S.M. El-Sayed. (2004). A numerical simulation and explicit solutions of the generalized Burger?Fisher equation. Appl. Math. Comput., 152, P. 403?413.
  19. Pankaj, R. D. (2013) Laplace - Modified Decomposition Method to Study Solitary Wave Solutions of Coupled Nonlinear Klein-Gordon Schr?dinger Equation, International Journal of Statistika and Mathematika, 5(1), pp 01-05
  20. H. He. (2006). some asymptotic methods for strongly nonlinear equations. Int. J. Modern Phys., B 20, 10, P. 1141?1199.
  21. M. Abulwafa, M.A. Abdou, A.A. Mahmoud. (2006). The solution of nonlinear coagulation problem with mass loss, Chaos Solitons Fract., 29 (2), P. 313?330.
  22. (2012). Multisoliton solutions to Cahn?Allen equation using double expfunction method. Phys. Wave Phenom., 20 (2), P. 118?121.
  23. Abdul-Majid Wazwaz. (2008). ?tanh?coth and the sine?cosine methods for kinks, solitons, and periodic solutions for the Pochhammer?Chree equations?. Appl. Math. Comput, 195 (1), P. 24?33.
  24. Kumar Arun, Pankaj R. D. (2015). Tanh?coth scheme for traveling wave solutions For Nonlinear Wave Interaction model. Journal of the Egyptian Mathematical Society, 23 (2), P. 282?285.

How to Cite This Article

Kavita Sharma, Arun Kumar and Ram Dayal Pankaj. (2017); DEVELOPMENT OF MODULATIONAL INSTABILITIES IN TRAVELING WAVE SOLUTIONS FOR WAVE-WAVE INTERACTION IN IONIC MEDIA., Int. J. of Adv. Res., 5 (04), 1323-1330, ISSN 2320-5407. DOI: https://doi.org/10.21474/IJAR01/3950

Corresponding Author

ARUN KUMAR
2Department of Mathematics, Government College Kota, Kota (Raj.), India
Creative Commons Attribution 4.0 This work is licensed under a Creative Commons Attribution 4.0 International License.