PL EN


Preferences help
enabled [disable] Abstract
Number of results
Journal
2014 | 12 | 7 | 480-489
Article title

Travelling wave solutions: A new approach to the analysis of nonlinear physical phenomena

Content
Title variants
Languages of publication
EN
Abstracts
EN
In this manuscript, a reliable scheme based on a general functional transformation is applied to construct the exact travelling wave solution for nonlinear differential equations. Our methodology is investigated by means of the modified homotopy analysis method which contains two convergence-control parameters. The obtained results reveal that the proposed approach is a very effective. Several illustrative examples are investigated in detail.
Publisher

Journal
Year
Volume
12
Issue
7
Pages
480-489
Physical description
Dates
published
1 - 7 - 2014
online
21 - 6 - 2014
Contributors
  • Department of Mathematics, Faculty of Basic Sciences, University of Malayer, Malayer, Iran
author
  • Department of Mathematics, Islamic Azad University, Najafabad Branch, Najafabad, Iran
References
  • [1] K. A. Gepreel, M. S. Mohamed, Chinese Phys. B 22, 010201 (2013) http://dx.doi.org/10.1088/1674-1056/22/1/010201[Crossref]
  • [2] K. A. Gepreel, S. Omran, Chinese Phys. 21, 110204 (2012) http://dx.doi.org/10.1088/1674-1056/21/11/110204[Crossref]
  • [3] K. A. Gepreel, Wseas Trans. Math. 7, 625 (2012)
  • [4] M. A. E. Herzallah, K. A. Gepreel, Appl. Math. Model. 36, 5678 (2012) http://dx.doi.org/10.1016/j.apm.2012.01.012[Crossref]
  • [5] K. A. Gepreel, S. M. Abo-Dahab, T. A. Nofal, Math. Prob. Eng. Doi: 2012:827901
  • [6] K. A. Gepreel, Appl. Math. Lett. 24, 1428 (2011) http://dx.doi.org/10.1016/j.aml.2011.03.025[Crossref]
  • [7] S. J. Liao, Beyond Perturbation: Introduction to Homotopy Analysis Method (Chapman Hall/CRC Press, Boca Raton, 2003 http://dx.doi.org/10.1201/9780203491164[Crossref]
  • [8] S. Abbasbandy, Nonlinear Analysis RWA 11, 307 (2010) http://dx.doi.org/10.1016/j.nonrwa.2008.11.005[Crossref]
  • [9] I. Pastor, V. M. Perez-Garcia, F. Encinas, J. M. Guerra, L. Vazquez, Physica D 66, 412 (1993) http://dx.doi.org/10.1016/0167-2789(93)90076-D[Crossref]
  • [10] S. Jimenez, L. Vazquez, Comput. Appl. Math. 12, 7 (1993)
  • [11] A. K. Golmankhaneh, N. A. Porghoveh, D. Baleanu, Rom. Rep. Phys. 350 (2013)
  • [12] X. J. Yang, D. Baleanu, W. P. Zhong, P. Romanian. Acad. A 14, 127 (2013)
  • [13] S. Abbasbandy, Y. Tan, S.J. Liao, Appl. Math. Comput. 188, 1794 (2007) http://dx.doi.org/10.1016/j.amc.2006.11.136[Crossref]
  • [14] A. Fakhari, D. Domairry, G. Ebrahimpour, Phys. Lett. A 368, 64 (2007) http://dx.doi.org/10.1016/j.physleta.2007.03.062[Crossref]
  • [15] F. M. Allan, Chaos Solitons Fract. 39, 1744 (2009) http://dx.doi.org/10.1016/j.chaos.2007.06.116[Crossref]
  • [16] A. S. Bataineh, M. S. M. Noorani, I. Hashim, Commun. Nonlinear Sci. 13, 2060 (2008) http://dx.doi.org/10.1016/j.cnsns.2007.05.026[Crossref]
  • [17] A. S. Bataineh, M. S. M. Noorani, I. Hashim, Commun. Nonlinear Sci. 14, 409 (2009) http://dx.doi.org/10.1016/j.cnsns.2007.10.007[Crossref]
  • [18] M. Ganjiani, H. Ganjiani, Nonlinear Dyn. 56, 159 (2009) http://dx.doi.org/10.1007/s11071-008-9386-7[Crossref]
  • [19] A. K. Alomari, M. S. M. Noorani, R. Nazar, Acta. Appl. Math. 108, 395 (2009) http://dx.doi.org/10.1007/s10440-008-9318-z[Crossref]
  • [20] Y. M. Chen, J. K. Liu, Acta Mech. Sin. 25, 707 (2009) http://dx.doi.org/10.1007/s10409-009-0256-4[Crossref]
  • [21] S. J. Liao, Ph.D. thesis, Shanghai Jiao Tong University (Shanghai, Chine,1992)
  • [22] H. Jafari, K. Sayevand, H. Tajadodi, D. Baleanu, Cent. Eur. J. Phys. 11(10), 1523 (2013) http://dx.doi.org/10.2478/s11534-013-0209-1[Crossref]
  • [23] S. J. Liao, Int. J. Non-linear Mech. 32, 815 (1997) http://dx.doi.org/10.1016/S0020-7462(96)00101-1[Crossref]
  • [24] S. J. Liao, Eng. Anal. Bound. Elem. 20, 91 (1997) http://dx.doi.org/10.1016/S0955-7997(97)00043-X[Crossref]
  • [25] S. J. Liao, Shanghai J. Mech. 18, 196 (1997)
  • [26] S. J. Liao, Int. J. Non-linear Dyn. 19, 93 (1999) http://dx.doi.org/10.1023/A:1008373627897[Crossref]
  • [27] M. Yamashita, K. Yabushita, K. Tsuboi, J. Phys. A 40, 8403 (2007) http://dx.doi.org/10.1088/1751-8113/40/29/015[Crossref]
  • [28] Y. Bouremel, Commun. Nonlinear. Sci. Numer. Simulat. 12, 714 (2007) http://dx.doi.org/10.1016/j.cnsns.2005.07.001[Crossref]
  • [29] L. Tao, H. Song, S. Chakrabarti, Clastal. Eng. 54, 825 (2007) http://dx.doi.org/10.1016/j.coastaleng.2007.05.008[Crossref]
  • [30] H. Song, L. Tao, J. Coast. Res. 50, 292 (2007)
  • [31] M. Sajid, T. Hayat, S. Asghar, Nonlinear Dyn. 50, 27 (2007) http://dx.doi.org/10.1007/s11071-006-9140-y[Crossref]
  • [32] I. Hashim, M. Chowdhury, Phys. Lett. A 372, 470 (2008) http://dx.doi.org/10.1016/j.physleta.2007.07.067[Crossref]
  • [33] K. A. A. Zahra, M. A. A.l Hussain, Int. Math. Forum. 6, 2349 (2011)
  • [34] A. Wazwaz, Appl. Math. Lett. 19, 1162 (2006) http://dx.doi.org/10.1016/j.aml.2005.07.014[Crossref]
  • [35] Y. Cherruault, Kybernetes 18, 31 (1989) http://dx.doi.org/10.1108/eb005812[Crossref]
  • [36] P. Sauceza, A. VandeWouwer, P. A. Zegelingc, J. Comput. Appl. Math. 183, 343 (2005) http://dx.doi.org/10.1016/j.cam.2004.12.028[Crossref]
Document Type
Publication order reference
Identifiers
YADDA identifier
bwmeta1.element.-psjd-doi-10_2478_s11534-014-0475-6
JavaScript is turned off in your web browser. Turn it on to take full advantage of this site, then refresh the page.