A symbolic computational method for constructing exact solutions to difference-differential equations

Applied Mathematics and Computation

Volumn 178, Issue 2, 2006, Pages 431-440

  Zhen, Wang ^a   Zhang, Hongqing ^a  

^a DALIAN UNIVERSITY OF TECHNOLOGY   (China)

Author keywords

Difference differential equation; Exact solutions; Soliton solutions; Toda equation

Indexed keywords

DIFFERENCE EQUATIONS; FUNCTION EVALUATION; NONLINEAR EQUATIONS; RICCATI EQUATIONS; SOLITONS;

DIFFERENCE-DIFFERENTIAL EQUATION; EXACT SOLUTIONS; SOLITON SOLUTIONS; TODA EQUATION;

COMPUTATIONAL METHODS;

EID: 33746253653     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2005.11.060     Document Type: Article

References (17)

1. Toda, and Kouichi. A search for higher-dimensional integrable modified KdV equation-the Painlevé approach, recent advances in integrable systems. J. Nonlin. Math. Phys. 9 (2002) 207-212
2. Knecht M., Pasquier R., and Pasquier J.-Y. Painlevé analysis and integrable properties of (2 + 1) nonrelativistic field theory. J. Math. Phys. 36 (1995) 4181-4191
3. Ablowitz M.J., and Segur H. Solitons and the Inverse Scattering Transform (1981), SIAM, Philadelphia
4. Weiss J., Tabor M., and Carnevale G. The Painlevé property for partial differential equations. J. Math. Phys. 24 (1983) 522-526
5. Fan E. A family of completely integrable multi-Hamiltonian systems explicitly related to some celebrated equations. J. Math. Phys. 42 (2001) 4327-4344
6. Olver P.J. Applications of Lie Groups to Differential Equations (1993), Springer, New York
7. Bluman G.W., and Kumei S. Symmetries and Differential Equations (1989), Springer, Berlin
8. Fuchssteiner B. Master symmetries, higher order time-dependent symmetries and conserved densities of nonlinear evolution equations. Progr. Theoret. Phys. 70 (1983) 1508-1524
9. Ablowitz M.J., and Clarkson P.A. Nonlinear Evolution Equations and Inverse Scattering (1991), Cambridge Univ. Press, Cambridge
10. Ablowitz M.J., and Ladik F.J. A nonlinear difference scheme and inverse scattering. Stud. Appl. Math. 55 (1976) 213-229
11. Grammaticos B., Ramani A., and Papageorgiou V.G. Do integrable mappings have the Painlevé property?. Phys. Rev. Lett. 67 (1991) 1825-1828
12. Capel H.W., Nijhoff F.W., and Papageorgiou V.G. Complete integrability of Lagrangian mappings and lattices of KdV type. Phys. Lett. A 155 (1991) 371-387
13. Conte R., and Musette M. Link between solitary waves and projective Riccati equations. J. Phys. A: Math. Gen. 25 (1992) 5609-5623
14. Bountis T.C., Papageorgiou V., and Winternitz P. On the integrability of systems of nonlinear ordinary differential equations with superposition principles. J. Math. Phys. 27 (1986) 1215
15. Kajiwara K., and Satsuma J. The conserved quantities and symmetries of the two-dimensional Toda lattice hierarchy. J. Math. Phys. 32 (1991) 506-514
16. Hu X.B., and Clarkson P.A. In: Clarkson P.A., and Niijhoff F.W. (Eds). Symmetries and Integrability of Difference Equations (1990), Cambridge Univ. Press, Berlin 15
17. Baldwin D., Götas U., and Hereman W. Symbolic computation of hyperbolic tangent solutions for nonlinear differential-difference equations. Comput. Phys. Commun. 162 (2004) 203-217