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钟形孤立子

Sine-Gordon方程是十九世纪发现的一种偏微分方程:

由于Sine-Gordon方程有多种孤立子解而倍受瞩目。

目录

孤立子解编辑

利用分离变数法可得Sine-Gordon方程的多种孤立子解[1]

扭型孤立子编辑

 

 

 
Sine-Gordon kink soliton plot1
 
Sine-Gordon kink soliton plot2

钟型孤立子编辑

Sine-Gordon方程有如下孤立子解:

 

其中

 
 
顺时针孤立子
 
反时针孤立子

双孤立子解编辑

 

 

 
Sine-Gordon colliding soltons plot1
 
Sine-Gordon colliding soltons plot2
 
Sine-Gordon bright & dark solitons plot1
 
& dark solitons plot2
 
扭型与反扭型碰撞
 
扭型-扭型碰撞
 
大振幅行波呼吸子
 
小振幅呼吸子

三孤立子解编辑

 
扭型行波呼吸子与驻波呼吸子碰撞
 
反扭型行波呼吸子与驻波波呼吸子碰撞

呼吸子解编辑

 
Sine-Gordon方程的呼吸子解
 

 

 

 
Sine-Gordon breather plot1
 
Sine-Gordon breather plot2

几何解释编辑

 
三维欧几里德空间的负常曲率曲面

sin-Gordon方程有一个几何解释:三维欧几里德空间的负常曲率曲面[2]

参考文献编辑

  1. ^ Inna Shingareva Carlos Lizarraga Celaya, Solving Nonlinear Partial Differential Equations with Maple and Mathematica, p86-94,Springer
  2. ^ 陈省身 Geometrical interpretation of the sinh-Gordon equation。annals Polonici Mathematici XXXIX 1981
  • Bour E (1862). "Théorie de la déformation des surfaces". J. Ecole Imperiale Polytechnique. 19: 1–48.
  • Rajaraman, R. (1989). Solitons and Instantons: An Introduction to Solitons and Instantons in Quantum Field Theory. North-Holland Personal Library. 15. North-Holland. pp. 34–45. ISBN 978-0-444-87047-6.
  • Polyanin, Andrei D.; Valentin F. Zaitsev (2004). Handbook of Nonlinear Partial Differential Equations. Chapman & Hall/CRC Press. pp. 470–492. ISBN 978-1-58488-355-5.
  • Dodd, Roger K.; J. C. Eilbeck, J. D. Gibbon, H. C. Morris (1982). Solitons and Nonlinear Wave Equations. London: Academic Press. ISBN 978-0-12-219122-0.
  • Georgiev DD, Papaioanou SN, Glazebrook JF (2004). "Neuronic system inside neurons: molecular biology and biophysics of neuronal microtubules". Biomedical Reviews 15: 67–75.
  • Georgiev DD, Papaioanou SN, Glazebrook JF (2007). "Solitonic effects of the local electromagnetic field on neuronal microtubules". Neuroquantology 5 (3): 276–291.