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单词 Lax pair
释义

Lax pair

中文百科

Lax 对

Lax 对定义。一个非线性偏微分方程

F(x,t,u,……)=0

的Lax 对 是一对线性微分算子

 L=L(u,\lambda)

 M=M(u,\lambda)

[L,M] =LM-ML 是交换子。

如果 F(x,t,u,……)=0 可以表示为 Lax 方程:

L_t+[L,M]=0,且 L \phi=\lambda(t) \phi,则 \lambda_t=0,并且  \phi 满足

\phi_t=M\phi

英语百科

Lax pair Lax 对

In mathematics, in the theory of integrable systems, a Lax pair is a pair of time-dependent matrices or operators that satisfy a corresponding differential equation, called the Lax equation. Lax pairs were introduced by Peter Lax to discuss solitons in continuous media. The inverse scattering transform makes use of the Lax equations to solve such systems.

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更新时间:2025/6/20 4:20:38