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Prog. Theor. Phys. 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^*

Department of Mathematics and Physics, Ritsumeikan University, Kyoto 603
^*Department of Applied Mathematics and Physics, Kyoto University, Kyoto 606

(Received September 3, 1976)

Abstract:

A Bäcklund transformation for the Boussinesq equation is given in the bilinear from. It is shown that the Bäcklund transformation generates an important class of nonlinear evolution equations exhibiting N-soliton solutions. They are a modified Boussinesq equation, a higher order water wave equation introduced by Kaup and a coupled equation whose N-soliton solution reduces to that of the nonlinear Schrödinger equation with normal dispersion. The relation between the Bäcklund transformation and the inverse scattering method is also discussed.

URL : http://ptp.ipap.jp/link?PTP/57/797/
DOI : 10.1143/PTP.57.797

[ Full Text PDF : FREE ACCESS (755K) ] Citation: Plain Text BiBTeX EndNote(RIS) RSS

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Citing Article(s) :

1. Journal of the Physical Society of Japan 66 (1997) pp. 2211-2213 :

   Construction of Bäcklund Transformations with Binary Bell Polynomials

   Franklin Lambert and Johan Springael

2. 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

3. Progress of Theoretical Physics Vol. 75 No. 5 (1986) pp. 1250-1253 :

   On the Inverse Problem and Bäcklund Transformation for the Nonlinear Equation u_xxx-(3/2)α²u²u_x+3∂_x^-1u_tt-3αu_x∂_x^-1u_t=0

   A. Roy Chowdhury and Siraj Ahmad

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