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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
[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
-
[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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