EVOLUTION OF MODULATIONAL INSTABILITY IN TRAVELLING WAVE SOLUTION OF NON-LINEAR PARTIAL DIFFERENTIAL EQUATION
Keywords:Jacobi Elliptic Functions, Ritz Variational Method, Spatially Periodic Trial Function
The Ritz variational method has been applied to the nonlinear partial differential equation to construct a model for travelling wave solution. The spatially periodic trial function was chosen in the form of combination of Jacobian Elliptic functions, with the dependence of its parameters
E. Kit and L. Shemer (2002) J. Fluid Mech. 450, 201–205. DOI: https://doi.org/10.1017/S0022112001006498
D. Anderson (1983) Phys. Rev. A 27 (6), 3135–3145.
N. J. Zabusky and M. D. Kruskal (1965) Phys. Rev. Lett. 15(6), 240–243. DOI: https://doi.org/10.1103/PhysRevLett.15.240
H. Airault, H. P. McKean, and J. Moser,Comm. (1977) PureAppl. Math. 30(1), 95–148.
E.R.Tracy, H.H.Chen and Y.C. Lee (1984) Phys. Rev. Lett. 53, 218 – 221.
B. Hafizi (1981) Phys.Fluids 24(10), 1791–1798.
Q. S. Chang, B. L. Guo, and H. Jiang (1995) Math. Comp. 64(210), 537–553, S7–S11.
A. O. Smirnov (1989) Mat.Zametki 45(6), 66–73, 111 (Russian).
M. Sigal, Comm. (1993) Math. Phys. 153(2), 297–320.
P. L. Christiansen, J. C. Eilbeck, V. Z. Enolskii, and N. A. Kostov, (1995)Proc. Roy.Soc. London Ser. A 451(1943), 685–700.
A.V. Porubov and D. F. Parker, (1999) Wave Motion 29(2), 97–109. DOI: https://doi.org/10.1016/S0165-2125(98)00033-X
F. F. Sun, (2003), Master’s thesis, National University, Singapore.
V. E. Zakharov and A. B. Shabat, Ž.Ėksper. (1971)Teoret. Fiz 61(1), 118–134, (1972) Soviet Physics JETP 34(1), 62–69.
Arun Kumar, (2009), International Journal of Computational and Applied Mathematics ISSN 1819-4966, 4(2) 159–164.
LIANG Zu-Feng, TANG Xiao-Yan,(2010) CHIN. PHYS. LETT. Vol. 27(3)030201.
Hirota R (1973) J. Math Phys. 14 805. DOI: https://doi.org/10.1063/1.1666399
Jiao X Y and Lou S Y (2009) Chin. Phys. Lett. 26 040202.
Zhao S L, Zhang D J and Chen D Y (2009) Chin. Phys. Lett.26 030202.
Gao Y, Tang X Y and Lou S Y (2009) Chin. Phys. Lett. 26 030502
Yang J R and Mao J J (2008) Chin. Phys. Lett. 25 1527
Yan T, Yu J L and Huang N N (2008) Chin. Phys. Lett. 2552
Tang X Y, Lou S Y and Zhang Y (2002) Phys.Rev.E 66046601
Tang X Y and Lou S Y (2003)J. Math. Phys. 44 4000
Tang X Y and Lou S Y (2009) Front. Phys. Chin. 2 235
Tang X Y and Liang Z F (2006) Phys. Lett.A 351 398
How to Cite
License and Copyright Agreement
In submitting the manuscript to the journal, the authors certify that:
- They are authorized by their co-authors to enter into these arrangements.
- The work described has not been formally published before, except in the form of an abstract or as part of a published lecture, review, thesis, or overlay journal.
- That it is not under consideration for publication elsewhere.
- That its release has been approved by all the author(s) and by the responsible authorities – tacitly or explicitly – of the institutes where the work has been carried out.
- They secure the right to reproduce any material that has already been published or copyrighted elsewhere.
- They agree to the following license and copyright agreement.
Authors who publish with International Journal of Engineering Technologies and Management Research agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License (CC BY-SA 4.0) that allows others to share the work with an acknowledgment of the work's authorship and initial publication in this journal.
- Authors can enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or edit it in a book), with an acknowledgment of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) before and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work.
For More info, please visit CopyRight Section