摘要Considering the bilinear form of a (3+1)-dimensional soliton equation, we obtain a bilinear Bäcklund transformation for the equation. As an application, soliton solution and stationary rational solution for the (3+1)-dimensional soliton equation are presented.
Abstract:Considering the bilinear form of a (3+1)-dimensional soliton equation, we obtain a bilinear Bäcklund transformation for the equation. As an application, soliton solution and stationary rational solution for the (3+1)-dimensional soliton equation are presented.
WU Jian-Ping. A Bilinear Bäcklund Transformation and Explicit Solutions for a (3+1)-Dimensional Soliton Equation[J]. 中国物理快报, 2008, 25(12): 4192-4194.
WU Jian-Ping. A Bilinear Bäcklund Transformation and Explicit Solutions for a (3+1)-Dimensional Soliton Equation. Chin. Phys. Lett., 2008, 25(12): 4192-4194.
[1] Ablowitz M J and Segur H 1981 Solitons and theInverse Scattering Transform (Philadelphia, PA: SIAM) [2] Novikov S P, Manakov S V , Pitaevskii L P and Zakharov VE 1984 Theory of Solitons, the Inverse Scattering Methods (NewYork: Consultants Bureau) [3] Matveev V B and Salle M A 1991 DarbouxTransformations and Solitons (Berlin: Springer) [4] Gu C H 1995 Soliton Theory and its Application(Berlin: Springer) [5] Hirota R 1971 Phys. Rev. Lett. {\bf 27 1192 [6] Hirota R and Satsuma J 1977 Prog. Theor. Phys. {\bf57 797 [7] Geng X G 2003 J. Phys. A: Math. Gen. {\bf 36 2289 [8] Geng X G and Ma Y L 2007 Phys. Lett. A {\bf 369 285 [9] Hirota R 2004 The Direct Method in Soliton Theory(Cambridge: Cambridge University Press)