New travelling wave solutions to the Boussinesq and the Klein-Gordon equations

Communications in Nonlinear Science and Numerical Simulation

Volumn 13, Issue 5, 2008, Pages 889-901

  Wazwaz, Abdul Majid ^a  

^a SAINT XAVIER UNIVERSITY   (United States)

Author keywords

Boussinesq equation; Extended tanh method; Klein Gordon equation; Periodic solutions; Solitons

Indexed keywords

COMPUTATIONAL METHODS; NONLINEAR EQUATIONS; NUMERICAL METHODS;

BOUSSINESQ EQUATION; EXTENDED TANH METHOD; KLEIN-GORDON EQUATION; NONLINEAR EVOLUTION EQUATION; TRAVELLING WAVE SOLUTION;

SOLITONS;

COMPUTATIONAL METHODS; NONLINEAR EQUATIONS; NUMERICAL METHODS; SOLITONS;

EID: 36248992919     PISSN: 10075704     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cnsns.2006.08.005     Document Type: Article

References (24)

1. Sirendaoreji. Auxiliary equation method and new solutions of Klein-Gordon equations. Chaos, Solitons & Fractals 31 4 (2007) 943-950
2. Sirendaoreji. A new auxiliary equation and exact travelling wave solutions of nonlinear equations. Phys Lett A 356 2 (2006) 124-130
3. Parker A, Dye JM. Boussinesq-type equations and switching solitons. In: Proc of institute of NAS of Ukraine 43(1); 2002: 344-51.
4. Yan Z. Constructing exact solutions for two-dimensional nonlinear dispersion Boussinesq equation. II: Solitary patterns solutions. Chaos, Solitons & Fractals 18 4 (2003) 869-880
5. Yan Z. New compacton soliton solutions and solitary patterns solutions of nonlinearly dispersive Boussinesq equations. Comput Phys Commun 149 1 (2002) 11-18
6. Yan Z. Abundant families of Jacobi elliptic function solutions of the (2 + 1)-dimensional integrable DaveyStewartson-type equation via a new method. Chaos, Solitons & Fractals 18 2 (2003) 299-309
7. Yan Z. Envelope compactons and solitary patterns. Phys Lett A 355 3 (2006) 212-215
8. Kaya D. Explicit solutions of generalized nonlinear Boussinesq equations. J Appl Math 1 1 (2001) 29-37
9. Polyanin A.D., and Zaitsev V.E. Handbook of Nonlinear Partial Differential Equations (2004), Chapman and Hall/CRC, Boca Raton
10. Khater A.H., and Hasan M.M. Travelling and periodic wave solutions of some nonlinear wave equations. Z. Naturforsch 59a 7/8 (2004) 389-396
11. Malfliet W. Solitary wave solutions of nonlinear wave equations. Am J Phys 60 7 (1992) 650-654
12. Malfliet W., and Hereman W. The tanh method: I. Exact solutions of nonlinear evolution and wave equations. Phys Scripta 54 (1996) 563-568
13. Malfliet W., and Hereman W. The tanh method: II. Perturbation technique for conservative systems. Phys Scripta 54 (1996) 569-575
14. Wazwaz A.M. The tanh method for travelling wave solutions of nonlinear equations. Appl Math Comput 154 3 (2004) 713-723
15. Wazwaz A.M. The tanh method: Exact solutions of the sine-Gordon and the sinh-Gordon equations. Appl Math Comput 49 (2005) 565-574
16. Wazwaz A.M. Partial differential equations: Methods and applications (2002), Balkema Publishers, The Netherlands
17. Wazwaz A.M. Solitary wave solutions for modified forms of the Degasperis-Procesi and Camassa-Holm and equations. Phys Lett A 352 (2006) 500-504
18. Wazwaz A.M. A study on nonlinear dispersive partial differential equations of compact and noncompact solutions. Appl Math Comput 135 2-3 (2003) 399-409
19. Wazwaz A.M. A construction of compact and noncompact solutions of nonlinear dispersive equations of even order. Appl Math Comput 135 2-3 (2003) 324-411
20. Wazwaz A.M. Compactons in a class of nonlinear dispersive equations. Math Comput Model 37 3/4 (2003) 333-341
21. Wazwaz A.M. Variants of the two-dimensional Boussinesq equations with compactons, solitons and periodic Solutions. Comput Math Appl 49 (2005) 295-301
22. Wazwaz A.M. New compactons, solitons and periodic solutions for nonlinear variants of the KdV and the KP equations. Chaos, Solitons & Compactons 22 1 (2004) 249-260
23. Wazwaz A.M. Special types of the nonlinear dispersive Zakharov-Kuznetsov equation with compactons, solitons and periodic solutions. Int J Comput Math 81 9 (2004) 1107-1119
24. Wazwaz A.M. A class of nonlinear fourth order variant of a generalized Camassa-Holm equation with compact and noncompact solutions. Appl Math Comput 165 (2005) 485-501