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

$\phi_t=M\phi$

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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Lax pair