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Exactly Solvable Nonlinear Evolution Equations Expressed by Trilinear Form

  • J. Matsukidaira
  • J. Satsuma
Conference paper
Part of the Research Reports in Physics book series (RESREPORTS)

Abstract

Hirota’s method is one of the powerfull ways to obtain exact solutions of soliton equations. It also serves as a tool to understand the structure of solutions. In fact, it has been revealed that almost all soliton equations are reduced to bilinear forms, which are equivalent to the identities of determinants[1]. The theory of τ function developed by Sato et al. strongly relies on this fact [2-5]. Then an interesting question is whether it is possible to extend the soliton equations from the point of view.

Keywords

Bilinear Form Young Diagram Nonlinear Evolution Equation Nonlinear Partial Differential Equation Boussinesq Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    R. Hirota, in Solitons, ed. by R. K. Bullough and P. J. Caudrey (Springer, Berlin, 1980).Google Scholar
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    M. Sato and Y. Sato, in Nonlinear Partial Differential Equations in Applied Science, ed. by H. Fujita, P. D. Lax and G. Strang (Kinokuniya/North Holland, Tokyo, 1983) 259.Google Scholar
  3. [3]
    E. Date, M. Jimbo, M. Kashiwara and T. Miwa, in Non-linear integrable Systems-Classical Theory and Quantum Theory, ed. by M. Jimbo and T. Miwa (World Scientific, Singapore, 1983) p. 39.Google Scholar
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    K. Ueno and K. Takasaki, Group Representation and Systems of Differential Equations, Adv. Stud, in Pure Math. 4(Kinokuniya, Tokyo, 1984) 1.Google Scholar
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    Y. Ohta, J. Satsuma, D. Takahashi and T. Tokihiro, Prog. Theor. Phys. Suppl. 94(1988) 210.MathSciNetADSCrossRefGoogle Scholar
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    J. Matsukidaira, J. Satsuma and W. Strampp, Phys. Lett. A. 147 (1990) 467.MathSciNetADSCrossRefGoogle Scholar
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    J. Matsukidaira and J. Satsuma, to appear in J. Phys. Soc. Jpn. (1990).Google Scholar
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    J. Matsukidaira and J. Satsuma, submitted to Phys. Lett. A.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • J. Matsukidaira
    • 1
  • J. Satsuma
    • 1
  1. 1.Department of Applied Physics, Faculty of EngineeringUniversity of TokyoBunkyo-ku, Tokyo 113Japan

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