关于双线性化Hirota-Satsuma方程的一点注记

A Note on the Bilinear Hirota-Satsuma Equation for Shallow Water Waves

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摘要从新的视角考虑Hirota双线性变换,建立了Hirota-Satsuma方程与其双线性化方程之间的局部等价性。提出了双线性化Hirota-Satsuma方程的由二阶微分方程加上适当的初值条件所定义的新型B覿cklund变换,并通过该变换从Hirota-Satsuma方程的种子解构造出其双线性化方程新的精确解。 By considering the Hirota bilinear transformation from a new point of view,the local equivalence between the Hirota-Satsuma equation and its bilinear equation is established.A new type of B？cklund transformation,which is defined by a second-order ODE along with the appropriate initial values,is presented to new exact solutions for the bilinear Hirota-Satsuma equation from the seed solutions of original Hirota-Satsuma equation.

作者蒋盈峰

机构地区江苏技术师范学院数理学院

出处《江苏技术师范学院学报》 2012年第4期60-63,共4页 Journal of Jiangsu Teachers University of Technology

基金国家自然科学基金青年基金(11102076)

关键词双线性化Hirota-Satsuma方程局部等价 Bcklund变换 bilinear Hirota-Satsuma equation local equivalence Backlund transformation

分类号 O175.4 [理学—基础数学]

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1Ablowitz M J, Clarkson P A. Solitons, Nonlinear Evolution Equations and Inverse Scattering [M].Cambridge:Cambridge University Press, 1991.
2Chen A H, Li X M. Darboux transformation and soliton solutions for Boussinesq-Burgers equation [J]. Chaos, Solitons and Fractals. 2006, 27: 43-49.
3Clarkson P A, Cosgrove C M. Painlev 6 analysis of the nonlinear Sehrodinger family of equations [J]. J. Phys. A: Math. Gen. 1987, 20: 2003-2024.
4He J H, Wu X H. Construction of solitary solution and compacton-like solution by variational iteration method [J]. Chaos, Solitons and Fractals. 2006, 29: 108-113.
5Hirota R, Satsuma J. N-soliton solutions of model equations for shallow water waves [J]. J. Phys. Soc. Jpn. 1976, 40:611-614.
6Hirota R, Satsuma J. Nolinear equations generated from the B~cklund transformation for the Boussinesq equation [J]. Prog. Theor. Phys. 1997, 57: 797-800.
7Clarkson P A, Mansfield E L.On a shallow water wave equation [J]. Nonlinearity. 1994,7: 975-1000.
8Satsuma J, Kaup D J. Backlund transformation in bilinear form to the Hirota-Satsuma equation [J]. J. Phys. Soc. Jpn. 1978, 43: 692-697.
9Zhang Y, Deng S F, Chen D Y. The novel muhi-soliton solutions of equation for shallow water waves [J]. J. Phys. Soc. Jpn. 2003, 72 (3): 763-764.
10Zhang Y, Chen D Y. Backlund transformation and soliton solutions for the shallow water wave equation [J]. Chaos, Solitons and Fractals. 2004, 20:343-351.

1于志云,苏婷.Hirota-Satsuma方程的Darboux变换解[J].河南科技大学学报（自然科学版）,2012,33(2):87-91.
2谷存昌,赵苗婵.Hirota-satsuma方程的Darboux变换[J].周口师范学院学报,2008,25(2):32-34.
3李姝敏,斯仁道尔吉.Hirota-Satsuma方程的复合型解(英文)[J].内蒙古师范大学学报（自然科学汉文版）,2010,39(4):331-335.
4张金顺,杨运平.Hirota-Satsuma方程的Darboux变换和孤子解(英文)[J].郑州大学学报（理学版）,2003,35(3):1-4.
5苏锦芬,高平.耗散Hirota-Satsuma方程的全局吸引子[J].广州大学学报（自然科学版）,2014,13(4):22-26.
6韩秀,徐英,吴娇.Wick型随机Hirota-Satsuma方程的精确解[J].徐州师范大学学报（自然科学版）,2008,26(1):26-29. 被引量：1
7郭婷婷.Hirota-Satsuma方程的Pfaffian化[J].太原师范学院学报（自然科学版）,2011,10(4):43-45.
8邓俊谦,杨瑞峰,张金顺.Hirota-Satsuma簇与精确解[J].河南师范大学学报（自然科学版）,2004,32(3):103-105.
9刘文健,刘希强,桑波.非线性发展方程的新精确解(英文)[J].西北师范大学学报（自然科学版）,2012,48(2):31-36. 被引量：8
10刘仰魁,彭昌宁,彭世林.Hirota—Satsuma方程的变换和孤波解[J].甘肃高师学报,2003,8(5):23-24.

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