Sinh-Gordon方程

Sinh-Gordon方程 是一个非线性偏微分方程：^[1]

${\displaystyle \varphi _{tt}-\varphi _{xx}=\sinh \varphi }$

解析解

${\displaystyle f1:={\frac {2}{\lambda }}\ln \tan {\frac {\lambda b(kx+\mu t+\theta )}{2{\sqrt {b\lambda (\mu ^{2}-ak^{2})}}}}}$

${\displaystyle f2:={\frac {-2}{\lambda }}\ln \tan {\frac {\lambda b(kx+\mu t+\theta )}{2{\sqrt {b\lambda (\mu ^{2}-ak^{2})}}}}}$

${\displaystyle f3:={\frac {2}{\lambda }}\arctan \exp {\frac {\lambda b(kx+\mu t+\theta )}{2{\sqrt {b\lambda (\mu ^{2}-ak^{2})}}}}}$

${\displaystyle f4:={\frac {-2}{\lambda }}\arctan \exp {\frac {\lambda b(kx+\mu t+\theta )}{2{\sqrt {b\lambda (\mu ^{2}-ak^{2})}}}}}$

行波图

Sinh-Gordon 方程行波图

Sinh-Gordon 方程行波图

Sinh-Gordon 方程行波图

Sinh-Gordon 方程行波图

参见

双重sinh-Gordon方程

参考文献

1. Andrei D. Polyanin,Valentin F. Zaitsev, HANDBOOK OF NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS,（《非线性偏微分方程手册》） SECOND EDITION p485 CRC PRESS

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