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给出一般非线性发展方程构造Wronskian解的间接法. 根据Young图运算的性质给出了文中命题的证明, 并讨论了置换群特征标与Young图表达式系数间的关系.
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关键词:
- 非线性发展方程 /
- Wronskian解 /
- Young图 /
- 特征标
In this paper, we give indirect methods constructed Wronskian solution of a general nonlinear evolution equations. Under the properties of the computing of Young diagram we have proved the proposition of this paper and discuss the relationship between the permutation group character and Young diagram expressions coefficient.-
Keywords:
- nonlinear evolution equations /
- Wronskian determinant solution /
- Young diagram /
- irreducible character
[1] Ablowitz M J, Clarkson P A 1991 Solitons, Nonlinear Evolution Equations and Inverse Scattering Transform (Cambridge: Cambridge University Press)
[2] Rogers C, Shadwick W R 1982 Bäcklund Transformation and Their Application (New York: Academic Press)
[3] Zhang H Q, Fan E G, Lin G 1998 Chin. Phys. 7 649
[4] Matveev V B, Salle M A 1991 Darboux Transformations and Solitons (Berlin: Springer)
[5] Hirota R 1971 Phys. Rev. Lett. 27 1192
[6] Freeman N C, Nimmo J J C 1983 Phys. Lett. A 95 1
[7] Hirota R, Tang 1986 J. Phys. Soc. Jpn. 55 2137
[8] Zhang S Q 2008 Acta Phys. Sin. 57 1335 (in Chinese) [张善卿 2008 物理学报 57 1335]
[9] OHTA Y 2003 J. Nonlinear Math. Phys. 10 143
[10] Bogoyavlenskii O I 1990 Lett. Nuovo. Cimento. Math. USSR. Izv. 34 245
[11] Toda K, Yu S J, Fukuyama F 1999 Rep. Math. Phys. 44 247
[12] Yan Z Y, Zhang H Q 2002 Comput. Math. Appl. 44 1430
[13] Tian B, Zhao K Y, Gao Y T 1997 Int. J. Engng. Sci. 35 1081
[14] Calogero F, Degasperis A 1976 Nuovo. Cimento. B 32 201
[15] Elwakil S A, El-labany S K, Zahran M A, Sabry R 2003 Z. Naturforsch. A 58 39
[16] Estvez P G, Hernaez G A 2000 J. Phys. A 33 2131
[17] Yan Z Y 2003 Czech. J. Phys. 53 89
[18] Gilson C R, Nimmo J J C 1993 Phys. Lett. A 180 337
[19] Qu C Z 1996 Theor. Phys. 25 369
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[1] Ablowitz M J, Clarkson P A 1991 Solitons, Nonlinear Evolution Equations and Inverse Scattering Transform (Cambridge: Cambridge University Press)
[2] Rogers C, Shadwick W R 1982 Bäcklund Transformation and Their Application (New York: Academic Press)
[3] Zhang H Q, Fan E G, Lin G 1998 Chin. Phys. 7 649
[4] Matveev V B, Salle M A 1991 Darboux Transformations and Solitons (Berlin: Springer)
[5] Hirota R 1971 Phys. Rev. Lett. 27 1192
[6] Freeman N C, Nimmo J J C 1983 Phys. Lett. A 95 1
[7] Hirota R, Tang 1986 J. Phys. Soc. Jpn. 55 2137
[8] Zhang S Q 2008 Acta Phys. Sin. 57 1335 (in Chinese) [张善卿 2008 物理学报 57 1335]
[9] OHTA Y 2003 J. Nonlinear Math. Phys. 10 143
[10] Bogoyavlenskii O I 1990 Lett. Nuovo. Cimento. Math. USSR. Izv. 34 245
[11] Toda K, Yu S J, Fukuyama F 1999 Rep. Math. Phys. 44 247
[12] Yan Z Y, Zhang H Q 2002 Comput. Math. Appl. 44 1430
[13] Tian B, Zhao K Y, Gao Y T 1997 Int. J. Engng. Sci. 35 1081
[14] Calogero F, Degasperis A 1976 Nuovo. Cimento. B 32 201
[15] Elwakil S A, El-labany S K, Zahran M A, Sabry R 2003 Z. Naturforsch. A 58 39
[16] Estvez P G, Hernaez G A 2000 J. Phys. A 33 2131
[17] Yan Z Y 2003 Czech. J. Phys. 53 89
[18] Gilson C R, Nimmo J J C 1993 Phys. Lett. A 180 337
[19] Qu C Z 1996 Theor. Phys. 25 369
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