Application of the exp-function method to nonlinear lattice differential equations for multi-wave and rational solutions

Mathematical Methods in the Applied Sciences

Volumn 34, Issue 14, 2011, Pages 1707-1710

  Aslan, Äsmail ^a  

^a IZMIR INSTITUTE OF TECHNOLOGY   (Turkey)

Author keywords

differential difference Korteweg de Vries equation; exp function method; lattice differential equations; traveling wave solutions

Indexed keywords

EXP-FUNCTION METHOD; KORTEWEG-DE VRIES EQUATIONS; LATTICE DIFFERENTIAL EQUATION; NONLINEAR LATTICES; RATIONAL SOLUTION; SOLUTION PROCEDURE; TRAVELING WAVE SOLUTION;

DIFFERENTIAL EQUATIONS; RATIONAL FUNCTIONS;

NONLINEAR EQUATIONS;

EID: 80052266360     PISSN: 01704214     EISSN: 10991476     Source Type: Journal    
DOI: 10.1002/mma.1476     Document Type: Article

References (29)

1. Toda M, Theory of Nonlinear Lattices. Springer: New York, 1989.
2. Wadati M, Transformation theories for nonlinear discrete systems. Progress of Theoretical Physics Supplement 1976; 59: 36-63.
3. Ablowitz MJ, Ladik J, Nonlinear differential-difference equation. Journal of Mathematical Physics 1975; 16: 598-603.
4. Hirota R, The Direct Method in Soliton Theory. Cambridge University Press: Cambridge, 2004.
5. He JH, Wu XH, Exp-function method for nonlinear wave equations. Chaos Solitons Fractals 2006; 30: 700-708.
6. Mohyud-Din ST, Noor MA, Waheed A, Exp-function method for generalized travelling solutions of Calogero-Degasperis-Fokas equation. Zeitschrift für Naturforschung A-A Journal of Physical Sciences 2010; 65: 78-84.
7. Ã-ziş T, Aslan Ä, Exact and explicit solutions to the (3 + 1)-dimensional Jimbo-Miwa equation via the Exp-function method. Physics Letters A 2008; 372: 7011-7015.
8. Aslan Ä, Generalized solitary and periodic wave solutions to a (2 + 1)-dimensional Zakharov-Kuznetsov equation. Applied Mathematics and Computation 2009; 217: 1421-1429.
9. Mohyud-Din ST, Solution of nonlinear differential equations by exp-function method. World Applied Sciences Journal 2009; 7: 116-147.
10. Aslan Ä, The Exp-function approach to the Schwarzian Korteweg-de Vries equation. Computers and Mathematics with Applications 2010; 59: 2896-2900.
11. Aslan Ä, Application of the Exp-function method to the (2 + 1)-dimensional Boiti-Leon-Pempinelli equation using symbolic computation. International Journal of Computer Mathematics 2011; 88: 747-761.
12. Zhu SD, Exp-function method for the hybrid-lattice system. International Journal of Nonlinear Sciences and Numerical Simulation 2007; 8: 461-464.
13. Zhang S, Application of Exp-function method to a KdV equation with variable coefficients. Physics Letters A 2007; 365: 448-453.
14. Dai CQ, Zhang JF, Application of He's Exp-function method to the stochastic mKdV equation. International Journal of Nonlinear Sciences and Numerical Simulation 2009; 10: 675-680.
15. Yomba E, Application of Exp-function method for a system of three component-Schrödinger equations. Physics Letters A 2009; 373: 4001-4011.
16. Marinakis V, The Exp-function method and n-soliton solutions. Zeitschrift für Naturforschung A 2008; 63: 653-656.
17. Zhang S, Zhang HQ, Exp-function method for N-soliton solutions of nonlinear evolution equations in mathematical physics. Physics Letters A 2009; 373: 2501-2505.
18. Aslan Ä, Multi-wave and rational solutions for nonlinear evolution equations. International Journal of Nonlinear Sciences and Numerical Simulation 2010; 11: 619-623.
19. Aslan Ä, Constructing rational and multi-wave solutions to higher order NEEs via the Exp-function method. Mathematical Methods in the Applied Sciences 2011; DOI: 10.1002/mma.1417.
20. Zhang S, Exp-function method: solitary, periodic and rational wave solutions of nonlinear evolution equations. Nonlinear Science Letters A 2010; 1: 143-146.
21. Mohyud-Din ST, Noor MA, Noor KI, Some relatively new techniques for nonlinear problems. Mathematical Problems in Engineering 2009; 25. Article ID 234849.
22. Ylrm A, Hosseini MM, Usman M, Mohyud-Din ST, On nonlinear sciences. Studies in Nonlinear Sciences 2010; 1: 97-117.
23. He JH, Some asymptotic methods for strongly nonlinear equations. International Journal of Modern Physics B 2006; 20: 1141-1199.
24. Hirota R, Satsuma J, A variety of nonlinear network equations generated from the Bäcklund transformation for the Toda lattice. Progress of Theoretical Physics Supplement 1976; 59: 64-100.
25. Hirota R, Nonlinear partial difference equations I: a difference analogue of the KdV equation. Journal of the Physical Society of Japan 1977; 43: 1429-1433.
26. Zhang Y, Zhao HQ, Li JB, The long wave limiting of the discrete nonlinear evolution equations. Chaos Solitons Fractals 2009; 42: 2965-2972.
27. Aslan Ä, Comment on: 'New exact solutions for the Kawahara equation using Exp-function method' [Journal of Computational and Applied Mathematics 2009; 233:97-102]. Journal of Computational and Applied Mathematics 2010; 234: 3213-3215.
28. Aslan Ä, Remark on: 'Exp-function method for the exact solutions of fifth order KdV equation and modified Burgers equation' [Applied Mathematics and Computation 2009. DOI: 10.1016/j.amc.2009.07.009 ]. Applied Mathematics and Computation 2010; 217: 2912.
29. Aslan Ä, Comment on: 'Application of Exp-function method for (3 + 1)-dimensional nonlinear evolution equations' [Computers and Mathematics with Applications 2008; 56:1451-1456]. Computers and Mathematics with Applications 2011; 61: 1700-1703.