The G′G method and topological soliton solution of the K(m,n) equation

Communications in Nonlinear Science and Numerical Simulation

Volumn 16, Issue 6, 2011, Pages 2377-2382

  Ebadi, Ghodrat ^a   Biswas, Anjan ^b  

^a UNIVERSITY OF TABRIZ   (Iran)

^b DELAWARE STATE UNIVERSITY   (United States)

Author keywords

G G method; Integrability; K(m,n) equation; Solitons

Indexed keywords

TOPOLOGY;

G METHODS; G′G METHOD; INTEGRABILITY; K(M,N) EQUATION; KDV EQUATION; SOLITON SOLUTIONS; TOPOLOGICAL SOLITON;

SOLITONS;

EID: 78651456274     PISSN: 10075704     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cnsns.2010.09.009     Document Type: Article

References (30)

1. Antonova M., Biswas A. Adiabatic parameter dynamics of perturbed solitary waves. Commun Nonlinear Sci Numer Simul 2009, 14(3):734-748.
2. Aslan I. A note on G′/G method again. Appl Math Comput 2010, 217:937-938.
3. Banerjee R.S. Painleve analysis of the K(m,n) equations which yield compactons. Phys Script 1998, 57(5):598-600.
4. Bekir A. Application of the G′G-expansion method for nonlinear evolution equations. Phys Lett A 2008, 372(19):3400-3406.
5. Biswas A. 1-Soliton solution of the K(m,n) equation with generalized evolution. Phys Lett A 2008, 372(25):4601-4602.
6. Biswas A. 1-Soliton solution of the K(m,n) equation with generalized evolution and time-dependent damping and dispersion. Comput Math Appl 2010, 59(8):2538-2542.
7. Bruzon M.S., Gandarias M.L. Classical potential symmetries of the K(m,n) equation with generalized evolution term. WSEAS Trans Math 2010, 9(4):275-284.
8. Bruzon MS, Gandarias ML. Travelling wave solutions of the K(m,n) equation with generalized evolution, Mathe Meth Appl Sci, submitted for publication.
9. Cenesiz Y., Keskin Y., Kurnaz A. The solution of nonlinear dispersive K(m,n) equation by RDT method. Int J Nonlinear Sci 2010, 9(4):461-467.
10. Demina M.V., Kudryashov N.A., Sinel'Shchikov D.I. The polygonal method for constructing exact solutions to certain nonlinear differential equations describing water waves. Comput Math Math Phys 2008, 48(12):2182-2193.
11. Dey B. Compacton solutions for a class of two parameter generalized odd-order Korteweg-de Vries equations. Phys Rev E 1998, 57(4):4733-4738.
12. Girgis L, Biswas A. A study of solitary waves by He's semi-inverse variational principle, Waves Random Complex Media, submitted for publication.
13. Heremant W., Takaoka M. Solitary wave solutions of nonlinear evolution and wave equations using a direct method and MACSYMA. J Phys A 1990, 23:4805-4822.
14. Kudryashov NA, Prilipko SG. Exact solutions of the generalized K(m,n) equations, Commun Nonlinear Sci Numer Simul, submitted for publication.
15. Kudryashov N.A. Simplest equation method to look forexact solutions of nonlinear partial differential equations. Chaos, Solitons Fractals 2005, 24(5):1217-1231.
16. Kudryashov N.A. On types of nonlinear integrable equations with exact solutions. Phys Lett A 1991, 155(4-5):269-275.
17. Kudryashov N.A., Loguinova N.B. Extended simplest equation method for nonlinear differential equations. Appl Math Comput 2008, 205:396-402.
18. Kudryashov N.A. Seven common errors in finding exact solutions of nonlinear differential equations. Commun Nonlinear Sci Numer Simul 2009, 14:3507-3529.
19. Kudryashov N.A., Loguinova N.B. Be careful with the exp-function method. Commun Nonlinear Sci Numer Simul 2009, 14(5):3507-3529.
20. Kudryashov NA, A note on G′/G expansion method. Appl Math Comput, submitted for publication.
21. Rosenau P., Hyman J.M. Compactons: solitons with finite wavelength. Phys Rev Lett 1993, 70:564-567.
22. Rosenau P. Nonlinear dispersion and compact structures. Phys Rev Lett 1994, 73:1737-1741.
23. Rosenau P. On solitons compactons and Lagrange maps. Phys Lett A 1996, 211(5):265-275.
24. Rosenau P. Compact and non-compact dispersive structures. Phys Lett A 2000, 275(3):193-203.
25. Triki H. Wazwaz A-M. Soliton solutions for the (2+1)-dimensional and (3+1)-dimensional K(m,n) equations. Appl Math Comput, submitted for publication.
26. Wang M.L., Li X.Z., Zhang J.L. The G′G-expansion method and travelling wave solutions of nonlinear evolution equations in mathematical physics. Phys Lett A 2008, 372(4):417-423.
27. Weinstein M.I. Solitary waves of nonlinear dispersive evolution equations with critical power nonlinearities. J Differ Eqn 1987, 69(2):192-203.
28. Zabusky N.J. Nonlinear Partial Differ Eqn 1965, 223-258. Academic, New York. W.F. Ames (Ed.).
29. Zayed E.M.E., Gepreel K.A. Some applications of the G′G-expansion method to non-linear partial differential equations. Appl Math Comput 2009, 212(1):1-13.
30. Zhang S., Tong J.L., Wang W. A generalized G′G-expansion method for the mKdV equation with variable coefficients. Phys Lett A 2008, 372(13):2254-2257.