The Exp-function approach to the Schwarzian Korteweg-de Vries equation

Computers and Mathematics with Applications

Volumn 59, Issue 8, 2010, Pages 2896-2900

  Aslan, Ismail ^a  

^a IZMIR INSTITUTE OF TECHNOLOGY   (Turkey)

Author keywords

Exp function method; Schwarzian Korteweg de Vries equation; Traveling wave solutions

Indexed keywords

EXACT TRAVELING WAVES; EXP-FUNCTION METHOD; KORTEWEG-DE VRIES EQUATIONS; PERIODIC WAVES; PHYSICAL SIGNIFICANCE; RATIONAL SOLUTION; TRAVELING WAVE SOLUTION;

EID: 77950188955     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.camwa.2010.02.007     Document Type: Article

References (24)

1. He J.H. An approximate solution technique depending on an artificial parameter: A special example. Commun. Nonlinear Sci. Numer. Simul. 3 (1998) 92-97
2. ′ / G)-expansion method and travelling wave solutions of nonlinear evolution equations in mathematical physics. Phys. Lett. A 372 (2008) 417-423
3. He J.H. A new approach to nonlinear partial differential equations. Commun. Nonlinear Sci. Numer. Simul. 2 (1997) 230-235
4. Liao S.J. Homotopy analysis method-a kind of nonlinear analytical technique not depending on small parameters. Shanghai J. Mech. 18 (1997) 196-200
5. Kudryashov N.A. Simplest equation method to look for exact solutions of nonlinear differential equations. Chaos Solitons Fractals 24 (2005) 1217-1231
6. Feng Z.S. The first-integral method to study the Burgers-Korteweg-de Vries equation. J. Phys. A: Math. Gen. 35 (2002) 343-349
7. He J.H. An elementary introduction to recently developed asymptotic methods and nanomechanics in textile engineering. Int. J. Mod. Phys. B. 22 (2008) 3487-3578
8. Dai Z.D., Wang C.J., Lin S.Q., Li D.L., and Mu G. The three-wave method for nonlinear evolution equations. Nonl. Sci. Lett. A 1 (2010) 77-82
9. He J.H., Wu G.C., and Austin F. The variational iteration method which should be followed. Nonl. Sci. Lett. A 1 (2010) 1-30
10. He J.H., and Wu X.H. Exp-function method for nonlinear wave equations. Chaos Solitons Fractals 30 (2006) 700-708
11. Zhu S.D. Exp-function method for the hybrid-lattice system. Int. J. Nonlinear Sci. Numer. Simul. 8 (2007) 461-464
12. Zhang S. Application of Exp-function method to a KdV equation with variable coefficients. Phys. Lett. A 365 (2007) 448-453
13. Dai C.Q., and Zhang J.F. Application of He's Exp-function method to the stochastic mKdV equation. Int. J. Nonlinear Sci. Numer. Simul. 10 (2009) 675-680
14. Öziş T., and Aslan İ. Exact and explicit solutions to the (3+1)-dimensional Jimbo-Miwa equation via the Exp-function method. Phys. Lett..A 372 (2008) 7011-7015
15. Aslan İ. Generalized solitary and periodic wave solutions to a (2 + 1)-dimensional Zakharov-Kuznetsov equation. Appl. Math. Comput. (2009) 10.1016/j.amc.2009.05.037
16. Yomba E. Application of Exp-function method for a system of three component-Schrödinger equations. Phys. Lett. A 373 (2009) 4001-4011
17. Marinakis V. The Exp-function method and n-soliton solutions. Z. Naturforsch. 63a (2008) 653-656
18. Zhang S., and Zhang H.Q. Exp-function method for N-soliton solutions of nonlinear evolution equations in mathematical physics. Phys. Lett. A 373 (2009) 2501-2505
19. Zhang S. Exp-function method: Solitary, periodic and rational wave solutions of nonlinear evolution equations. Nonl. Sci. Lett. A 1 (2010) 143-146
20. Fu H.M., and Dai Z.D. Double Exp-function method and application. Int. J. Nonlinear Sci. Numer. Simul. 10 (2009) 927-933
21. Ablowitz M.J., and Clarkson P.A. Solitons, Nonlinear Evolution Equations and Inverse Scattering (1991), Cambridge University Press, Cambridge
22. Krichever I.M., and Novikov S.P. Holomorphic bundles over algebraic curves and non-linear equation. Russian Math. Surveys 35 (1980) 53-79
23. Weiss J. The Painleve property for partial differential equations. J. Math. Phys. 24 (1983) 1405-1413
24. Ovsienko V., and Tabachnikov S. What is the Schwarzian derivative?. Notices Amer. Math. Soc. 56 1 (2009) 35-36