The tan h method: Solitons and periodic solutions for the Dodd-Bullough-Mikhailov and the Tzitzeica-Dodd-Bullough equations

Chaos, Solitons and Fractals

Volumn 25, Issue 1, 2005, Pages 55-63

  Wazwaz, Abdul Majid ^a  

^a SAINT XAVIER UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY CONDITIONS; BOUNDARY VALUE PROBLEMS; FLOW OF FLUIDS; FUNCTIONS; MATHEMATICAL MODELS; MATHEMATICAL TRANSFORMATIONS; QUANTUM THEORY;

BOUSSINESQ EQUATION; COMPACTON; PEAKON; PERIODIC SOLUTIONS;

SOLITONS;

EID: 13544272576     PISSN: 09600779     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.chaos.2004.09.122     Document Type: Article

References (28)

1. J.K. Perring, and T.H. Skyrme A model unified field equation Nucl. Phys. 31 1962 550 555
2. 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
3. N.J. Zabusky, and M.D. Kruskal Interaction of solitons in a collision less plasma and the recurrence of initial states Phys. Rev. Lett. 15 1965 240 243
4. M. Wadati Introduction to solitons Pramana: J. Phys. 57 5-6 2001 841 847
5. M. Wadati The exact solution of the modified Kortweg-de Vries equation J. Phys. Soc. Jpn. 32 1972 1681 1687
6. M. Wadati The modified Kortweg-de Vries equation J. Phys. Soc. Jpn. 34 1973 1289 1296
7. M. Wadati, H. Sanuki, and K. Konno Relationship among inverse method, Bäcklund transformation and an infinite number of conservation laws Prog. Theor. Phys. 53 1975 419 436
8. M. Wadati, and K. Sawada New representation of the soliton solution for the Korteweg-de Vries equation J. Phys. Soc. Jpn. 48 1980 312 318
9. M. Wadati, and K. Sawada Application of the trace method to the modified Korteweg-de Vries equation J. Phys. Soc. Jpn. 48 1980 319 325
10. K. Ohkuma, and M. Wadati The Kadomtsev-Petviashvili equation: The trace method and the soliton resonances J. Phys. Soc. Jpn. 52 1983 749 760
11. A.P. Fordy Soliton Theory: A Survey of Results 1990 MUP Manchester
12. A.C. Newell Solitons in Mathematics and Physics 1985 SIAM Philadelphia
13. S.P. Novikov, S.V. Manakov, L.P. Pitaevskii, and V.E. Zakharov Theory of Solitons 1984 Plenum NY
14. W. Malfliet Solitary wave solutions of nonlinear wave equations Am. J. Phys. 60 7 1992 650 654
15. Malfliet W., The tan h method: I. Exact solutions of nonlinear evolution and wave equations, Phys. Scr. 54, 563-8
16. Malfliet W., The tan h method: II. Perturbation technique for conservative systems, Phys. Scr. 54, 569-75
17. A.M. Wazwaz Partial Differential Equations: Methods and Applications 2002 Balkema Publishers The Netherlands
18. 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
19. 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
20. 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
21. A.M. Wazwaz A study of nonlinear dispersive equations with solitary-wave solutions having compact support Math. Comput. Simul. 56 2001 269 276
22. 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
23. 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
24. A.M. Wazwaz Construction of soliton solutions and periodic solutions of the Boussinesq equation by the modified decomposition method Chaos, Solitons & Fractals 12 8 2001 1549 1556
25. A.M. Wazwaz A computational approach to soliton solutions of the Kadomtsev-Petviashili equation Appl. Math. Comput. 123 2 2001 205 217
26. A.M. Wazwaz, and An analytic study of compactons structures in a class of nonlinear dispersive equations Math. Comput. Simul. 63 1 2003 35 44
27. A.M. Wazwaz Existence and construction of compacton solutions Chaos, Solitons & Fractals 19 3 2004 463 470
28. A.M. Wazwaz Compactons in a class of nonlinear dispersive equations Math. Comput. Modell. 37 3/4 2003 333 341