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International Workshop on Mathematics Mechanization

International Workshop on Geometric Invariance and Applications in Engineering

IWMM 2004, GIAE 2004: Computer Algebra and Geometric Algebra with Applications pp 163–178Cite as

Hamiltonian System and Algebro-Geometric Solution Associated with Dispersive Long Wave Equation

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3519))

Abstract

By using an iterative algebraic method, we derive from a spectral problem a hierarchy of nonlinear evolution equations associated with dispersive long wave equation. It is shown that the hierarchy is integrable in Liouville sense and possesses bi-Hamiltonian structure. Under a Bargmann constraint the spectral is nonlinearized to a completely integrable finite dimensional Hamiltonian system. By introducing the Abel-Jacobi coordinates, an algebro-geometric solution for the dispersive long wave equation is derived by resorting to the Riemann theta function.

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References

  1. Magri, F.: J. Math. Phys. 19, 1156–1162 (1978)

    Article  MATH  MathSciNet  Google Scholar 

  2. Magri, F.: Lectures Notes in Physics. 120th edn. Springer, Berlin (1980)

    Google Scholar 

  3. Olver, P.J.: Applications of Lie groups to differential equations. Springer, Berlin (1986)

    MATH  Google Scholar 

  4. Gel’fand, I.M., Dorfman, I.Y.: Funct. Anal. Appl.  15, 173–187 (1981)

    Google Scholar 

  5. Nutku, Y.: J. Math. Phys. 28, 2579 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  6. Tu, G.Z.: J. Math. Phys. 30, 330 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  7. Tu, G.Z.: J. Phys. A: Math. Gen. 22, 2375 (1989)

    Article  MATH  Google Scholar 

  8. Tu, G.Z.: J. Phys. A: Math. Gen. 23, 3903 (1990)

    Article  MATH  Google Scholar 

  9. Fan, E.G.: J. Math. Phys. 42, 4327 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  10. Fan, E.G.: Acta Math. Appl. Sin. 18, 405 (2002)

    Article  MATH  Google Scholar 

  11. Fan, E.G.: Phys. Lett. A 274, 135 (2000)

    Article  MathSciNet  Google Scholar 

  12. Cao, C.W.: Sci. in China A 33, 528 (1990)

    MATH  Google Scholar 

  13. Cao, C.W., Geng, X.G.: J. Phys. A 23, 4117 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  14. Geng, X.G.: J. Math. Phys. 34, 805 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  15. Geng, X.G.: Physica A 180, 241 (1992)

    MathSciNet  Google Scholar 

  16. Qiao, Z.J.: J. Phys. A 26, 4407 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  17. Qiao, Z.J.: J. Math. Phys. 34, 3110 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  18. Zeng, Y.B.: Phys. Lett. A 160, 541 (1991)

    Article  MathSciNet  Google Scholar 

  19. Zeng, Y.B.: Physica D 73, 171 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  20. Zeng, Z.B.: J. Phys. A 30, 3719 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  21. Novikov, S.P.: Funct. Anal. Appl. 8, 236 (1974)

    Article  MATH  Google Scholar 

  22. Dubrovin, B.A.: Funct. Anal. Appl.  9, 41 (1975)

    Google Scholar 

  23. Its, A., Matveev, V.: Funct. Anal. Appl. 9, 69 (1975)

    Article  MathSciNet  Google Scholar 

  24. Belokolos, E., Bobenko, A., Enol’skij, V., Its, A., Matveev, V.: Algebro-Geometrical Approach to Nonlinear Integrable Equations. Springer, Berlin (1994)

    Google Scholar 

  25. Christiansen, P.L., Eilbeck, J.C., Enolskii, V.Z., Kostov, N.A.: Proc. R. Soc. London A Math. 451, 685 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  26. Alber, M.S., Fedorov, Y.N.: Inverse Probl. 17, 1017 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  27. Porubov, A.V., Paeker, D.F.: Wave Motion 29, 97 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  28. Gesztesy, F., Holden, H.: Soliton Equations and Their Algebro-Geometric Solutions. Cambridge University Press, Cambridge (2003)

    Book  MATH  Google Scholar 

  29. Zhou, R.G.: J. Math. Phys. 38, 2535 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  30. Cao, C.W., Wu, Y.T., Geng, X.G.: J. Math. Phys. 40, 3948 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  31. Qiao, Z.J.: Reviews in Math. Phys. 13, 545 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  32. Cao, C.W., Geng, X.G., Wang, H.Y.: J. Math. Phys. 43, 621 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  33. Whitham, G.B.: Proc. R. Soc. A 299, 6 (1983)

    Article  Google Scholar 

  34. Broer, L.T.F.: Appl. Sci. Res. 31, 377 (1983)

    Article  MathSciNet  Google Scholar 

  35. Kupershmidt, B.A.: Commun. Math. Prhys. 99, 51 (1983)

    Article  MathSciNet  Google Scholar 

  36. Wang, M.L., Zhou, Y.B., Li, Z.B.: Phys. Lett. A 216, 67 (1983)

    Article  Google Scholar 

  37. Ruan, H.Y., Lou, S.Y.: Commun. Theor. Phys. 20, 73 (1993)

    MathSciNet  Google Scholar 

  38. Levi, D., Sym, A., Wojciechowsk, S.: J. Phys. A 16, 2423 (1983)

    Article  MATH  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Institute of Mathematics, Fudan University, Shanghai, 200433, P. R. China

    Engui Fan

Authors
  1. Engui Fan
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Editor information

Editors and Affiliations

  1. Key Laboratory of Mathematics Mechanization, Academy of Mathematics and Systems Science, CAS, P.O. Box, 100080, Beijing, P.R. China

    Hongbo Li

  2. School of Mathematics, University of Minnesota, 55455, Minneapolis, MN, U.S.A.

    Peter J. Olver

  3. Institute of Computer Science, Christian-Albrecht-University, 24098, Kiel, Germany

    Gerald Sommer

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© 2005 Springer-Verlag Berlin Heidelberg

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Fan, E. (2005). Hamiltonian System and Algebro-Geometric Solution Associated with Dispersive Long Wave Equation. In: Li, H., Olver, P.J., Sommer, G. (eds) Computer Algebra and Geometric Algebra with Applications. IWMM GIAE 2004 2004. Lecture Notes in Computer Science, vol 3519. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11499251_14

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  • DOI: https://doi.org/10.1007/11499251_14

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-26296-1

  • Online ISBN: 978-3-540-32119-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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