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齊次蒙日-安培方程

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齊次蒙日-安培方程(Homogeneous Monge-Ampère equation)是一個常見於黎曼幾何的非線性偏微分方程,同時也是卡拉比-丘流形證明時曾用的工具。[1] 廣義而言,定義兩個獨立變量x,y,以及一個非獨立變量u,蒙日-安培方程可以表述為:

這裏的A,B,C,D,E為一階變量x,y,ux和uy唯一的非獨立函數。

解析解

根據齊次蒙日-安培方程:
其對應的解析解為:

行波圖

Homogeneous Monge-Ampere equation plot
Homogeneous Monge-Ampere equation plot
Homogeneous Monge-Ampere equation plot
Homogeneous Monge-Ampere equation plot
Homogeneous Monge-Ampere equation plot
Homogeneous Monge-Ampere equation plot
Homogeneous Monge-Ampere equation plot
Homogeneous Monge-Ampere equation plot
Homogeneous Monge-Ampere equation plot
Homogeneous Monge-Ampere equation plot
Homogeneous Monge-Ampere equation plot
Homogeneous Monge-Ampere equation plot

參考文獻

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