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Prog. Theor. Phys. Vol. 51 No. 5 (1974) pp. 1355-1367

A Method for Finding N-Soliton Solutions of the K.d.V. Equation and K.d.V.-Like Equation

Katuro Sawada and Takeyasu Kotera

Department of Physics, Tokyo University of Education, Tokyo

(Received November 29, 1973)

Abstract:

To find N-soliton solutions of the K.d.V. equation, a method which can be also applicable to the so-called K.d.V.-like equation is presented. This equation belongs to another series than the class of equations solvable by inverse scattering method for Schrödinger equation.

URL : http://ptp.ipap.jp/link?PTP/51/1355/
DOI : 10.1143/PTP.51.1355

[ Full Text PDF : FREE ACCESS (727K) ] Citation: Plain Text BiBTeX EndNote(RIS) RSS

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References:

1. C. S. Gardner, J. M. Greene, M. D. Kruskal and R. M. Miura, Phys. Rev. Lett. 19 (1967), 1095[APS].
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4. R. Hirota, J. Math. Phys. 14 (1973), 807[AIP Scitation].
   For other references, see references therein.
5. T. Kotera and K. Sawada, preprint TUETP-73-18.
6. P. D. Lax, Commun. Pure Appl. Math. 21 (1968), 467.
7. E. Hopf, Commun. Pure Appl. Math. 3 (1950), 201.
   J. D. Cole, Quart. Appl. Math. 9 (1951), 225.
8. J. M. Burgers, Adv. Appl. Mech. 1 (1948), 171.

Citing Article(s) :

1. Journal of the Physical Society of Japan 58 (1989) pp. 2285-2296 :

   Soliton Solutions to the BKP Equations. I. the Pfaffian technique

   Ryogo Hirota

2. Journal of the Physical Society of Japan 59 (1990) pp. 3093-3100 :

   Properties of Conservation Laws of Nonlinear Evolution Equations

   Yoshimasa Matsuno

3. Journal of the Physical Society of Japan 59 (1990) pp. 4188-4189 :

   Towards an Extension of the Sawada Kotera Hierarchy

   F. Lambert and R. Willox

4. Journal of the Physical Society of Japan 61 (1992) pp. 1817-1818 :

   On the Fifth-Order Polynomial Evolution Equations of Not Normal Type and Miura Transformations

   Masaaki Ito

5. Journal of the Physical Society of Japan 65 (1996) pp. 2797-2806 :

   Pfaffian Representation of Solutions to the Discrete BKP Hierarchy in Bilinear Form

   Satoshi Tsujimoto and Ryogo Hirota

6. Journal of the Physical Society of Japan 67 (1998) pp. 772-777 :

   A Bäcklund Transformation and Nonlinear Superposition Formula of the Caudrey-Dodd-Gibbon-Kotera-Sawada Hierarchy

   Xing-Biao Hu and Robin Bullough

7. Journal of the Physical Society of Japan 68 (1999) pp. 46-50 :

   Generalized Lattice KdV Type Equation – Reduction of the Lattice W ₃ Algebra

   Kazuhiro Hikami

8. Journal of the Physical Society of Japan 76 (2007) 124004 (4 pages) :

   On Periodic Wave Solution and Asymptotic Property of KdV–Sawada–Kotera Equation

   Zhen-Yun Qin

9. Journal of the Physical Society of Japan 80 (2011) 045002 (2 pages) :

   The Vector Ito–Drienfel'd–Sokolov System: Bilinear Bäcklund Transformation and Lax Pair

   Maxim Ju. Balakhnev

10. Progress of Theoretical Physics Vol. 68 No. 4 (1982) pp. 1082-1104 :

    The Lie Algebra Structure of Degenerate Hamiltonian and Bi-Hamiltonian Systems

    Benno Fuchssteiner

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 Vol. 83 No. 3 (1990) pp. 395-413 :

    Action-Angle Representation of Multisolitons by Potentials of Mastersymmetries

    Gudrun Oevel, Benno Fuchssteiner and Maciej Blaszak

13. 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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