Analytic study on nonlinear variants of the RLW and the PHI-four equations

Communications in Nonlinear Science and Numerical Simulation

Volumn 12, Issue 3, 2007, Pages 314-327

  Wazwaz, Abdul Majid ^a  

^a SAINT XAVIER UNIVERSITY   (United States)

Author keywords

Compactons; PHI four equation; RLW equation; Sine cosine method; Solitary patterns solutions; Solitons; The tanh method

Indexed keywords

NONLINEAR EQUATIONS; SOLITONS;

COMPACTONS; PHI-FOUR EQUATION; RLW EQUATION; SINE-COSINE METHOD; SOLITARY PATTERNS; TANH METHOD;

PARTIAL DIFFERENTIAL EQUATIONS;

NONLINEAR EQUATIONS; PARTIAL DIFFERENTIAL EQUATIONS; SOLITONS;

EID: 33750495011     PISSN: 10075704     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cnsns.2005.03.001     Document Type: Article

References (24)

1. Dye J.M., and Parker A. An inverse scattering scheme for the regularized long-wave equation. J Math Phys 41 5 (2000) 2889-2904
2. Benjamin R.T., Bona J.L., and Mahony J.J. Model equations for long waves in nonlinear dispersive systems. Philos Trans Roy Soc London 272 (1972) 47-78
3. Ablowitz M.J., and Clarkson P.A. Solitons, nonlinear evolution equations and inverse scattering (1991), Cambridge University Press, Cambridge
4. Hereman W., and Takaoka M. Solitary wave solutions of nonlinear evolution and wave equations using a direct method and MACSYMA. J Phys A 23 (1990) 4805-4822
5. Zabusky N.J., and Kruskal M.D. Interaction of solitons in a collisionless plasma and the recurrence of initial states. Phys Rev Lett 15 (1965) 240-243
6. Wadati M. Introduction to solitons. Pramana: J Phys 57 5-6 (2001) 841-847
7. Wadati M. The modified Korteweg-de Vries equation. J Phys Soc Japan 34 (1973) 1289-1296
8. Kadomtsev B.B., and Petviashvili V.I. On the stability of solitary waves in weakly dispersive media. Sov Phys Dokl 15 (1970) 539-541
9. Zakharov V.E., and Kuznetsov E.A. On three-dimensional solitons. Soviet Phys 39 (1974) 285-288
10. Rosenau P., and Hyman J.M. Compactons: solitons with finite wavelengths. Phys Rev Lett 70 5 (1993) 564-567
11. Wazwaz A.M. A sine-cosine method for handling nonlinear wave equations. Math Comput Model 40 (2004) 499-508
12. Wazwaz A.M. Partial differential equations: methods and applications (2002), Balkema Publishers, The Netherlands
13. Wazwaz A.M. New solitary-wave special solutions with compact support for the nonlinear dispersive K(m,n) equations. Chaos, Solitons & Fractals 13 2 (2002) 321-330
14. Wazwaz A.M. 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
15. Wazwaz A.M. A study of nonlinear dispersive equations with solitary-wave solutions having compact support. Math Comput Simul 56 (2001) 269-276
16. Wazwaz A.M. Compactons dispersive structures for variants of the K(n, n) and the KP equations. Chaos, Solitons & Fractals 13 5 (2002) 1053-1062
17. Wazwaz A.M. Compactons and solitary patterns structures for variants of the KdV and the KP equations. Appl Math Comput 139 1 (2003) 37-54
18. Wazwaz A.M. A computational approach to soliton solutions of the Kadomtsev-Petviashili equation. Appl Math Comput 123 2 (2001) 205-217
19. Wazwaz A.M. An analytic study of compactons structures in a class of nonlinear dispersive equations. Math Comput Simul 63 1 (2003) 35-44
20. Wazwaz A.M., and Taha T. Compact and noncompact structures in a class of nonlinearly dispersive equations. Math Comput Simul 62 1-2 (2003) 171-189
21. Wazwaz A.M. The tanh method for travelling wave solutions of nonlinear equations. Appl Math Comput 154 3 (2004) 713-723
22. Malfliet W. The tanh method: a tool for solving certain classes of nonlinear evolution and wave equations. J Comput Appl Math 164-165 (2004) 529-541
23. Malfliet W. Solitary wave solutions of nonlinear wave equations. Am J Phys 60 7 (1992) 650-654
24. Malfliet W., and Hereman W. The Tanh Method: II. Perturbation technique for conservative systems. Phys Scr 54 (1996) 569-575