Some recent results on integrable Bilinear equations

Journal of Nonlinear Mathematical Physics

Volumn 8, Issue SUPPL., 2001, Pages 149-155

  Hu, Xing Biao ^a   Tam, Hon Wah ^b  

^a INSTITUTE OF COMPUTATIONAL MATHEMATICS AND SCIENTIFIC ENGINEERING COMPUTING   (China)

^b HONG KONG BAPTIST UNIVERSITY   (Hong Kong)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0037765177     PISSN: 14029251     EISSN: None     Source Type: Journal    
DOI: 10.2991/jnmp.2001.8.s.26     Document Type: Conference Paper

References (22)

1. Hirota R, Exact Solution of the Korteweg-de Vries Equation for Multiple Collisions of Solitons, Phys. Rev. Lett., 1971, V.27, 1192.
2. Hirota R, Direct Methods in Soliton Theory, in Solitons, Editors R K Bullough and P J Caudrey, Springer, Berlin, 1980.
3. Hirota R and Satsuma J, A Variety of Nonlinear Network Equations Generated from the Bäcklund Transformation for the Toda Lattice, Prog. Theor. Phys. Suppl., 1976, N 59, 64.
4. Matsuno Y, Bilinear Transformation Method, Academic, New York, 1984.
5. Nimmo J J C, Hirota's Method, in Soliton Theory, A Survey of Results, Editor A P Fordy, Manchester University Press, Manchester, 1990.
6. Miura R M (Editor), Bäcklund Transformations, in Lecture Notes in Mathematics, Vol.515, Springer, Berlin, 1976.
7. Rogers C and Shadwick W F, Bäcklund Transformations and Their Applications, Vol.161, in Mathematics in Science and Engineering, Academic Press, New York, 1982.
8. Hietarinta J, A Search for Bilinear Equations Passing Hirota's Three-Soliton Condition, J. Math. Phys., 1987, V.28, 1732.
9. Hu X-B, Clarkson P A and Bullough R, New Integrable Differential- Difference Systems, J. Phys. A: Math. Gen., 1997, V.30, L669-L676.
10. Belov A A and Chaltikian K D, Lattice Analogues of W-algebras and Classical Integrable Equations, Phys. Lett. B, 1993, V.309, 268-274.
11. Hu X-B and Zhu Z-N, A Bäcklund Transformation and Nonlinear Superposition Formula for the Belov-Chaltikian Lattice, J. Phys. A: Math. Gen., 1998, V.31, 4755-4761.
12. Blaszak M and Marciniak K, r-matrix Approach to Lattice Integrable Systems, J. Math. Phys., 1994, V.35, 4661-4682.
13. Hu X-B and Zhu Z-N, Some New Results on the Blaszak-Marciniak Lattice: Bäcklund Transformation and Nonlinear Superposition Formula, J. Math. Phys., 1998, V.39, 4766.
14. Ruijsenaars S N M, Relativistic Toda Systems, Comm. Math. Phys., 1990, V.133, 217-247.
15. Bruschi M and Ragnisco O, Recursion Operator and Bäcklund Transformations for the Ruijsenaars-Toda Lattice, Phys. Lett. A, 1988, V.129, 21-25
16. Lax Representation and Complete Integrability for the Periodic Relativistic Toda Lattice, 1989, V.134, 365-370.
17. Hietarinta J and Satsuma J, The Trilinear Equation as a (2 + 2)-Dimensional Extension of the (1 + 1)-Dimensional Relativistic Toda Lattice, Phys. Lett. A, 1991, V.161, 267-273.
18. Hu X-B and Wu Y-T, Application of the Hirota Bilinear Formalism to a New Integrable Differential-Difference Equation, Phys. Lett. A, 1998, V.246, 523-529.
19. Wu Y-T and Hu X-B, A New Integrable Differential-Difference System and Its Explicit Solutions, J. Phys. A: Math. Gen., 1999, V.32, 1515-1521.
20. Hu X-B, Wu Y-T and Geng X-G, Hirota Bilinear Approach to a New Integrable Differential- Difference System, J. Math. Phys., 1999, V.40, 2001-2010; 1999, V.40, 4180.
21. Narita K, Soliton Solution to Extended Volterra Equation, J. Phys. Soc. Japan, 1982, V.51, 1682-1685.
22. Hu X-B and Bullough R, Bäcklund Transformation and Nonlinear Superposition Formula of an Extended Lotka-Volterra Equation, J. Phys. A: Math. Gen., 1997, V.30, 3635-3641.