Generalized tanh method with symbolic computation and generalized shallow water wave equation

Computers and Mathematics with Applications

Volumn 33, Issue 4, 1997, Pages 115-118

  Gao, Yi Tian ^a   Tian, Bo ^a  

^a LANZHOU UNIVERSITY   (China)

Author keywords

(2+1) dimensional generalization of the shallow water wave equations; Generalized tanh method; Mathematical methods in physics; Soliton like solutions; Symbolic computation

Indexed keywords

ALGORITHMS; COMPUTATIONAL METHODS; FUNCTIONS; MATHEMATICAL MODELS; NUMERICAL METHODS; PROBLEM SOLVING; SOLITONS; SPECTRUM ANALYSIS;

GENERALIZED TANH METHODS; RIEMANN HILBERT PROBLEMS; SHALLOW WATER WAVE EQUATIONS;

NONLINEAR EQUATIONS;

EID: 0031069499     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0898-1221(97)00011-4     Document Type: Article

References (17)

1. H. Lan and K. Wang, Exact solutions for some coupled nonlinear equations: I, J. Phys. A 23, 3923-3928 (1990).
2. H. Lan and K. Wang, Exact solutions for some coupled nonlinear equations: II, J. Phys. A 23, 4097-4105 (1990).
3. S. Lou, G. Huang and H. Ruan, Exact solitary waves in a converting fluid, J. Phys. A 24, L587-L590 (1991).
4. A. Jeffrey and M. Mohamad, Exact solutions to the KdV-Burgers' equation, Wave Motion 14, 369-375 (1991).
5. B. Lu, Z. Pan, B. Qu and X. Jiang, Solitary wave solutions for some systems of coupled nonlinear equations, Phys. Lett. A 180, 61-64 (1993).
6. W. Ma, Travelling wave solutions to a seventh order generalized KdV equation, Phys. Lett. A 180, 221-224 (1993).
7. W. Zhang, A class of solitary wave solutions for the B-MKdV equation and the B-MBBM equation, (in Chinese), J. Lanzhou Univ. (Natural Sci.) 29 (3), 14-19 (1993).
8. A. Porubov, Exact travelling wave solutions of nonlinear evolution equation of surface waves in a convecting fluid, J. Phys. A 26, L797-L800 (1993).
9. E. Parkes, Exact solutions to the two-dimensional KdV equation, J. Phys. A 27, L497-L501 (1994).
10. B. Tian and Y.T. Gao, On the generalized tanh method for the (2+1)-dimensional breaking soliton equation, Mod. Phys. Lett. A 10, 2937 (1995).
11. B. Tian and Y.T. Gao, Beyond travelling waves: A new algorithm for solving nonlinear evolution equations, Computer Phys. Comm. 95, 139 (1996).
12. M. Jimbo and T. Miwa, Solitons and infinite-dimensional Lie algebras, Publ. Res. Inst. Math. Sci., Kyoto Univ. 19, 943-1001 (1983).
13. M. Boiti, J. Leon, M. Manna and F. Pempinelli, On the spectral transform of a KdV equation in two spatial dimensions, Inverse Problems 2, 271-279 (1986).
14. B. Dorizzi, B. Gammaticos, A. Ramani and P. Winternitz, Are all the equations of the KP hierarchy integrable?, J. Math. Phys. 27, 2848-2852 (1986).
15. O. Bogoyavlenskii, Overturning solitons in two-dimensional integrable equations, Russian Math. Surveys 45, 1-86 (1990).
16. P. Clarkson and E. Mansfield, On a shallow water wave equation, Nonlinearity 7, 975-1000 (1994).
17. B. Tian and Y.T. Gao, Soliton-like solutions for a (2+1)-dimensional generalization of the shallow water wave equations, Chaos, Solitons & Fractals (1996) (to appear).