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基于mKdV-sine-Gordon方程的Wronsk解的形式和结构,提出了Wronsk形式展开法,通过这一方法求得了该方程的丰富的相互作用解,该方法的主要特征是不要求Wronsk行列式元素满足线性偏微分方程组。
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关键词:
- mKdV-sine-Gordon方程 /
- Wronsk技巧 /
- 相互作用解 /
- Jacobi椭圆函数
In this paper, based on the forms and structures of Wronskian solutions of the mKdV-sine-Gordon equation, a Wronskian form expansion method is presented to find abundant interaction solutions of the mKdV-sine-Gordon equation. One characteristic of the method is that Wronskian entries don’t satisfy linear partial differential equations.-
Keywords:
- mKdV-sine-Gordon equation /
- Wronsk technique /
- interaction solutions /
- Jacobi elliptic function
[1] Ablowitz M J, Clarkson P A 1991 Soliton, Nonlinear Evolution Equations and Inverse Scattering (Cambridge: Cambridge University Press)
[2] Miura R M 1978 Bcklund Transformation (Berlin: Springer)
[3] Hirota R 2004 Direct Method in Soliton Theory (Cambridge: Cambridge University Press)
[4] Freeman N C, Nimmo J J C 1983 Phys. Lett. A 95 1
[5] Nimmo J J C, Freeman N C 1983 Phys. Lett. A 95 4
[6] Ma W X, You Y C 2005 Trans. Amer. Math. Soc. 357 1753
[7] Chen D Y, Zhang D J, Bi J B 2007 Sci. Chin. Ser. A 37 1335 (in Chinese)[陈登远、张大军、毕金钵 2007 中国科学A辑 37 1335]
[8] Ma W X 2002 Phys. Lett.A 301 35
[9] Zhang D J, Deng S F, Chen D Y 2004 Acta Math. Sci. 24A 257 (in Chinese)[张大军、邓淑芳、陈登远 2004 数学 24A 257]
[10] Gu C H 1986 Lett. Math. Phys. 12 31
[11] Konno K, Kameyama W, Sanuki H 1974 J. Phys. Soc. Jpn. 37 171
[12] Chen D Y, Zhang D J, Deng S F 2002 J. Phys. Soc. Jpn. 71 658
[13] Zhang D J, Deng S F 2002 J. Shanghai Univ. (Nat. Sci.) 8 232 (in Chinese)[张大军、邓淑芳 2002 上海大学学报(自然科学版) 8 232]
[14] Wang D M 2001 Elimination Methods (New York: Springer-Verlag Wien)
[15] Liu S K, Fu Z T, Liu S D, Zhao Q 2001 Acta Phys. Sin. 50 2068 (in Chinese) [刘式适、傅遵涛、刘式达、赵 强 2001 50 2068]
[16] Guo G P, Zhang J F 2002 Acta Phys. Sin. 51 1159 (in Chinese)[郭冠平、张解放 2002 51 1159]
[17] He F, Guo Q B, Liu L 2007 Acta Phys. Sin. 56 4326 (in Chinese)[贺 锋、郭启波、刘 辽 2007 56 4326]
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[1] Ablowitz M J, Clarkson P A 1991 Soliton, Nonlinear Evolution Equations and Inverse Scattering (Cambridge: Cambridge University Press)
[2] Miura R M 1978 Bcklund Transformation (Berlin: Springer)
[3] Hirota R 2004 Direct Method in Soliton Theory (Cambridge: Cambridge University Press)
[4] Freeman N C, Nimmo J J C 1983 Phys. Lett. A 95 1
[5] Nimmo J J C, Freeman N C 1983 Phys. Lett. A 95 4
[6] Ma W X, You Y C 2005 Trans. Amer. Math. Soc. 357 1753
[7] Chen D Y, Zhang D J, Bi J B 2007 Sci. Chin. Ser. A 37 1335 (in Chinese)[陈登远、张大军、毕金钵 2007 中国科学A辑 37 1335]
[8] Ma W X 2002 Phys. Lett.A 301 35
[9] Zhang D J, Deng S F, Chen D Y 2004 Acta Math. Sci. 24A 257 (in Chinese)[张大军、邓淑芳、陈登远 2004 数学 24A 257]
[10] Gu C H 1986 Lett. Math. Phys. 12 31
[11] Konno K, Kameyama W, Sanuki H 1974 J. Phys. Soc. Jpn. 37 171
[12] Chen D Y, Zhang D J, Deng S F 2002 J. Phys. Soc. Jpn. 71 658
[13] Zhang D J, Deng S F 2002 J. Shanghai Univ. (Nat. Sci.) 8 232 (in Chinese)[张大军、邓淑芳 2002 上海大学学报(自然科学版) 8 232]
[14] Wang D M 2001 Elimination Methods (New York: Springer-Verlag Wien)
[15] Liu S K, Fu Z T, Liu S D, Zhao Q 2001 Acta Phys. Sin. 50 2068 (in Chinese) [刘式适、傅遵涛、刘式达、赵 强 2001 50 2068]
[16] Guo G P, Zhang J F 2002 Acta Phys. Sin. 51 1159 (in Chinese)[郭冠平、张解放 2002 51 1159]
[17] He F, Guo Q B, Liu L 2007 Acta Phys. Sin. 56 4326 (in Chinese)[贺 锋、郭启波、刘 辽 2007 56 4326]
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