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应用数学学报  2013, Vol. 36 Issue (4): 727-737    DOI:
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Bell多项式在经典Boussinesq方程中的应用
魏小然, 薛玲玲
中国矿业大学(北京)理学院, 北京, 100083
Bilinear Bäcklund Transformation for Classical Boussinesq Equation
WEI Xiaoran, XUE Lingling
Department of Mathematics, China University of Mining and Technology, Beijing, 100083
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摘要 本文借助于Bell多项式研究经典Boussinesq方程, 将其转换成Hirota双线性形式, 构造了带参数的Bäcklund变换, 进而重新导出了其Lax表示.
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魏小然
薛玲玲
关键词经典Boussinesq方程   Bell 多项式   Hirota 双线性形式   Bäcklund变换   Lax对     
Abstract: The classical Boussinesq equation is revisited. By means of Bell polynomials, this equation is bilinearized. Furthermore, a Bäcklund transformation, consisting of four equations with an essential parameter, is constructed for it. Also, its Lax pair is recovered.
Key wordsclassical Boussinesq equation   Bell polynomial   Hirota bilinear form   Bäcklund transformation   Lax pair   
收稿日期: 2011-11-11;
基金资助:国家自然科学基金(10731080, 10971222, 11271366);中央高校基本科研资助项目
引用本文:   
魏小然,薛玲玲. Bell多项式在经典Boussinesq方程中的应用[J]. 应用数学学报, 2013, 36(4): 727-737.
WEI Xiaoran,XUE Lingling. Bilinear Bäcklund Transformation for Classical Boussinesq Equation[J]. Acta Mathematicae Applicatae Sinica, 2013, 36(4): 727-737.
 
[1] Nakamura A, Hirota R. A New Example of Explode-decay Solitary Waves in One-dimension. J. Phys. Soc. Japan, 1985, 54(2): 491-499
[2] Bell E T. Exponential Polynomials. Ann. Math., 1934, 35(2): 258-277
[3] Comtet L. Advanced Combinatorics. Dordrecht: Reidel, 1974
[4] Riordan J. Combinatorial Identities. New York: Wiley, 1968
[5] Gilson C, Lambert F, Nimmo J, Willox R. On the Combinatorics of the Hirota D-operators. Proc. R. Soc. Lond. A, 1996, 452: 223-234
[6] Lambert F, Springael J. Classical Darboux Transformations and the KP Hierarchy. Inv. Prob., 2001, 17(4): 1067-1074
[7] Lambert F, Springael J, Colin S, Willox R. An Elementary Approach to Hierarchies of Soliton Equations. J. Phys. Soc. Japan, 2007, 76: 054005
[8] Lambert F, Springael J. Soliton Equations and Simple Combinatorics. Acta. Appl. Math., 2008, 102: 147-178
[9] Fan E. New Bilinear Bäcklund Transformation and Lax Pair for the Supersymmetric Two-Boson Equation. Stud. Appl. Math., 2011, 127(3): 284-301
[10] Leo R A, Mancarella G, Soliani G. On the Broer-Kaup Hydrodynamical System. J. Phys. Soc. Japan, 1988, 57(3): 753-756
[11] Kupershimdit B A. Mathematics of Dispersive Water Waves. Commun. Math. Phys., 1985, 99(1): 51-73
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