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Prog. Theor. Phys. Vol. 52 No. 5 (1974) pp. 1498-1512

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A New Form of Bäcklund Transformations and Its Relation to the Inverse Scattering Problem

Ryogo Hirota

RCA Research Laboratories, Inc., 971-2 Aza 4-go, Zushi-machi, Machida-City, Tokyo 194-02

(Received March 5, 1974)

Abstract:

We present a new form of Bäcklund transformations which gives a unified method of finding Bäcklund transformations for solutions of certain nonlinear evolution equations and constructing the inverse scattering problem for solving the initial-value problem. We consider the sine-Gordon equation, the modified Korteweg-de Vries equation and the Korteweg-de Vries equation as examples.


URL : http://ptp.ipap.jp/link?PTP/52/1498/
DOI : 10.1143/PTP.52.1498

[ Full Text PDF : FREE ACCESS (914K) ] Citation:

References:

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Citing Article(s) :

  1. Journal of the Physical Society of Japan 56 (1987) pp. 3491-3498 :
    The 3+1 Dimensional Toda Equation and its Exact Solutions
    Akira Nakamura
  2. Journal of the Physical Society of Japan 57 (1988) pp. 3309-3322 :
    Exact Cylindrical Soliton Solutions of the Sine-Gordon Equation, the Sinh-Gordon Equation and the Periodic Toda Equation
    Akira Nakamura
  3. Journal of the Physical Society of Japan 58 (1989) pp. 412-422 :
    A Bilinear N-Soliton Formula for the KP Equation
    Akira Nakamura
  4. Journal of the Physical Society of Japan 60 (1991) pp. 1835-1838 :
    Bilinear, Pfaffian and Legendre Function Structuresof the Tomimatsu-Sato Solutionsof the Ernst Equation in General Relativity
    Akira Nakamura and Yasuhiro Ohta
  5. Journal of the Physical Society of Japan 61 (1992) pp. 3007-3008 :
    Bilinear Structures of the Painlevé II Equation and Its Solutions for Half Integer Constants
    Akira Nakamura
  6. Journal of the Physical Society of Japan 61 (1992) pp. 4295-4313 :
    Similarity KP Equation and Various Different Representations of Its Solutions
    Yasuhiro Ohta* and Akira Nakamura
  7. Journal of the Physical Society of Japan 70 (2001) pp. 605-608 :
    On the Hirota Representation of Soliton Equations with One Tau-Function
    Franklin Lambert, Ignace Loris, Johan Springael and Ralph Willox
  8. Progress of Theoretical Physics Vol. 53 No. 2 (1975) pp. 419-436 :
    Relationships among Inverse Method, Bäcklund Transformation and an Infinite Number of Conservation Laws
    Miki Wadati, Heiji Sanuki and Kimiaki Konno
  9. Progress of Theoretical Physics Vol. 55 No. 6 (1976) pp. 2037-2038 :
    Nonlinear Evolution Equations Generated from the Bäcklund Transformation for the Toda Lattice
    Ryogo Hirota and Junkichi Satsuma
  10. Progress of Theoretical Physics Vol. 57 No. 3 (1977) pp. 797-807 :
    Nonlinear Evolution Equations Generated from the Bäcklund Transformation for the Boussinesq Equation
    Ryogo Hirota and Junkichi Satsuma
  11. Progress of Theoretical Physics Vol. 70 No. 1 (1983) pp. 85-92 :
    A Comment on Bäcklund Transformations Connected with the Sturm-Liouville Operator
    W. Strampp and K.-H. Briz
  12. Progress of Theoretical Physics Supplement No.59 (1976) pp. 64-100 :
    A Variety of Nonlinear Network Equations Generated from the Bäcklund Transformation for the Toda Lattice
    Ryogo Hirota and Junkichi Satsuma

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