Sine-Gordon方程

Sine-Gordon方程是十九世纪发现的一种偏微分方程：

孤立子解

扭型孤立子

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

钟型孤立子

Sine-Gordon方程有如下孤立子解：

 顺时针孤立子 反时针孤立子

双孤立子解

 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
 驻波呼吸子 大振幅行波呼吸子 小振幅呼吸子

三孤立子解

 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

Sine-Gordon方程的呼吸子解

 Sine-Gordon breather plot1 Sine-Gordon breather plot2

几何解释

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

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
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