The tanh and the sine-cosine methods for compact and noncompact solutions of the nonlinear Klein-Gordon equation

Applied Mathematics and Computation

Volumn 167, Issue 2, 2005, Pages 1179-1195

  Wazwaz, Abdul Majid ^a  

^a SAINT XAVIER UNIVERSITY   (United States)

Author keywords

Compactons; Klein Gordon equation; Periodic solutions; Sine cosine method; Solitons; The tanh method

Indexed keywords

MATHEMATICAL TECHNIQUES;

COMPACTONS; KLEIN-GORDON EQUATION; PERIODIC SOLUTIONS; SINE-COSINE METHOD; THE TANH METHOD;

NONLINEAR EQUATIONS;

EID: 25144449613     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2004.08.006     Document Type: Article

References (32)

1. D.B. Duncan Symplectic finite difference approximations of the nonlinear Klein-Gordon equation SIAM J. Numer. Anal. 34 5 1997 1742 1760
2. J.K. Perring, and T.H. Skyrme A model unified field equation Nucl. Phys. 31 1962 550 555
3. M.J. Ablowitz, B.M. Herbst, and C. Schober On the numerical solution of the Sine-Gordon equation J. Comput. Phys. 126 1996 299 314
4. N.J. Zabusky, and M.D. Kruskal Interaction of solitons in a collisionless plasma and the recurrence of initial states Phys. Rev. Lett. 15 1965 240 243
5. M. Wadati Introduction to solitons Pramana: J. Phys. 57 5-6 2001 841 847
6. M. Wadati The exact solution of the modified Kortweg-de Vries equation J. Phys. Soc. Jpn. 32 1972 1681 1687
7. A.P. Fordy Soliton Theory: A Survey of Results 1990 MUP Manchester
8. A.C. Newell Solitons in Mathematics and Physics 1985 SIAM Philadelphia
9. S.P. Novikov, S.V. Manakov, L.P. Pitaevskii, and V.E. Zakharov Theory of Solitons 1984 Plenum New York
10. Y.S. Kivshar, and D.E. Pelinovsky Self-focusing and transverse instabilities of solitary waves Phys. Rep. 331 2000 117 195
11. B.B. Kadomtsev, and V.I. Petviashvili Sov. Phys. JETP 39 1974 285 295
12. W. Hereman, and M. Takaoka Solitary wave solutions of nonlinear evolution and wave equations using a direct method and MACSYMA J. Phys. A 23 1990 4805 4822
13. P. Rosenau, and J.M. Hyman Compactons: solitons with finite wavelengths Phys. Rev. Lett. 70 5 1993 564 567
14. S. Dusuel, P. Michaux, and M. Remoissenet From kinks to compactonlike kinks Phys. Rev. E 57 2 1998 2320 2326
15. A. Ludu, and J.P. Draayer Patterns on liquid surfaces: cnoidal waves, compactons and scaling Physica D 123 1998 82 91
16. W. Malfliet Solitary wave solutions of nonlinear wave equations Am. J. Phys. 60 7 1992 650 654
17. W. Malfliet The tanh method: I. Exact solutions of nonlinear evolution and wave equations Phys. Scr. 54 1996 563 568
18. W. Malfliet The tanh method: II. Perturbation technique for conservative systems Phys. Scr. 54 1996 569 575
19. A.M. Wazwaz The tanh method for travelling wave solutions of nonlinear equations Appl. Math. Comput. 154 3 2004 713 723
20. A.M. Wazwaz Partial Differential Equations: Methods and Applications 2002 Balkema Publishers The Netherlands
21. A.M. Wazwaz New solitary-wave special solutions with compact support for the nonlinear dispersive K(m, n) equations Chaos, Solitons Fractals 13 2 2002 321 330
22. A.M. Wazwaz Exact specific solutions with solitary patterns for the nonlinear dispersive K(m, n) equations Chaos, Solitons Fractals 13 1 2001 161 170
23. A.M. Wazwaz General compactons solutions for the focusing branch of the nonlinear dispersive K(n, n) equations in higher dimensional spaces Appl. Math. Comput. 133 2/3 2002 213 227
24. A.M. Wazwaz General solutions with solitary patterns for the defocusing branch of the nonlinear dispersive K(n, n) equations in higher dimensional spaces Appl. Math. Comput. 133 2/3 2002 229 244
25. A.M. Wazwaz Compactons dispersive structures for variants of the K(n, n) and the KP equations Chaos, Solitons Fractals 13 5 2002 1053 1062
26. A.M. Wazwaz Compactons and solitary patterns structures for variants of the KdV and the KP equations Appl. Math. Comput. 139 1 2003 37 54
27. A.M. Wazwaz A study on nonlinear dispersive partial differential equations of compact and noncompact solutions Appl. Math. Comput. 135 2-3 2003 399 409
28. A.M. Wazwaz A construction of compact and noncompact solutions of nonlinear dispersive equations of even order Appl. Math. Comput. 135 2-3 2003 324 411
29. A.M. Wazwaz Compactons in a class of nonlinear dispersive equations Math. Comput. Modell. 37 3/4 2003 333 341
30. A.M. Wazwaz Distinct variants of the KdV equation with compact and noncompact structures Appl. Math. Comput. 150 2004 365 377
31. A.M. Wazwaz Variants of the generalized KdV equation with compact and noncompact structures Comput. Math. Appl. 47 2004 583 591
32. A.M. Wazwaz New compactons, solitons and periodic solutions for nonlinear variants of the KdV and the KP equations Chaos, Solitons Fractals 22 2004 249 260