吉本斯-查理夫方程

吉本斯-查理夫方程(Gibbons-Tsarev equation)是一个非线性偏微分方程：^[1]

${\displaystyle u_{t}u_{xt}-u_{x}u_{tt}+u_{xx}+1=0}$

解析解

${\displaystyle u(x,t)=-(1/2)*x^{2}+_{C}1*x+_{C}2}$

${\displaystyle u(x,t)=exp(_{c}[2]*x)*_{C}1/_{c}[2]+x/_{c}[2]+_{C}2+(1/2)*_{c}[2]*t^{2}+_{C}3*t+_{C}4}$

${\displaystyle u(x,t)=-(1/2)*(_{C}3+_{C}1*x+_{C}2*t)^{2}/_{C}1^{2}+(_{C}3+_{C}1*x+_{C}2*t)*_{C}2+_{C}3}$

行波图

Gibsons-Tsarev equation traveling wave plot

Gibsons-Tsarev equation traveling wave plot

Gibsons-Tsarev equation traveling wave plot

Gibsons-Tsarev equation traveling wave plot 4

Gibsons-Tsarev equation traveling wave plot 5

参考文献

1. Andrei D. Polyanin,Valentin F. Zaitsev, HANDBOOK OF NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS, SECOND EDITION p764 CRC PRESS

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