Approximate solutions of coupled Ramani equation by using RDTM with compared DTM and exact solutions
Abstract
In this paper, we present a new approximate solutions
of famous coupled Ramani Equation. In order to obtain the solution, we use the
semi-analytical methods differential transform method (DTM) and reduced form of
DTM called reduced differential transform method (RDTM). We compare the RDTM
solutions with exact solution and DTM. Numerical results show clearly that DTM
and RDTM are very effective and also provide very accurate solutions. Also, one
can conclude that RDTM is used easier than DTM and converges faster than the
DTM for these kind of problems.
Keywords
Kaynakça
- Ramani A., Inverse scattering, ordinary differential equations of Painleve-type and Hirota’s bilinear formalism. In: Fourth International Conference Collective Phenomena, New York: Academy of Sciences (1981), p. 54.
- Hirota R., Direct method of finding exact solutions of nonlinear evolution equations, In: Bullough R., Caudrey P., editors. Backlund transformations, Berlin, Springer (1980), p. 1157-75.
- Hu X. B., Wang D. L., Tam H. W., Lax pairs and backlund transformations for a coupled Ramani equation and its related system, Applied Mathematics Letters (2000), 13, 45-48.
- Zhao J. X., Tam H. W., Soliton solutions of a coupled Ramani equation, Appl Math Lett, 16 (2006), 307-313.
- Ablowitz M. J., Clarkson P. A., Solitons, nonlinear evolution equations and inverse scattering transform, Cambridge University press, 1990.
- Ito M., An extension of nonlinear evolution equations K-dV (mK-dV) type to higher order, J. Physc. Soc. Jpn. (1980), 49 (2), 771-778.
- Zhang H., New exact traveling wave solutions for some nonlinear evolution equations, Chaos Solitons and Fractals (2005), 26 (3), 921-5.
- Feng Z., Traveling solitary wave solutions to evolution equations with nonlinear terms any order, Chaos Solitons and Fractals (2003), 17 (5), 861-8.
Ayrıntılar
Birincil Dil
İngilizce
Konular
-
Bölüm
Araştırma Makalesi
Yayımlanma Tarihi
31 Aralık 2016
Gönderilme Tarihi
28 Nisan 2016
Kabul Tarihi
21 Temmuz 2016
Yayımlandığı Sayı
Yıl 2016 Cilt: 4 Sayı: 4