变形KdV-Burgers方程

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变形KdV-Burgers(Modified KdV-Burgers equation)是一个非线性偏微分方程:[1]

u_{t}+u_{xxx}-\alpha*u^2*u_{x}-\beta*u_{xx}=0

解析解[编辑]

u(x, t) = -(1/6)*\beta*\sqrt(6)/\sqrt(\alpha)-\sqrt(6)*_C2*cot(_C1+_C2*x+(-2*_C2^3+(1/6)*\beta^2*_C2)*t)/\sqrt(\alpha)
u(x, t) = -(1/6)*\beta*\sqrt(6)/\sqrt(\alpha)-\sqrt(6)*_C2*coth(_C1+_C2*x+(2*_C2^3+(1/6)*\beta^2*_C2)*t)/\sqrt(\alpha)
u(x, t) = -(1/6)*\beta*\sqrt(6)/\sqrt(\alpha)+\sqrt(6)*_C2*tan(_C1+_C2*x+(-2*_C2^3+(1/6)*\beta^2*_C2)*t)/\sqrt(\alpha)
u(x, t) = -(1/6)*\beta*\sqrt(6)/\sqrt(\alpha)-\sqrt(6)*_C2*tanh(_C1+_C2*x+(2*_C2^3+(1/6)*\beta^2*_C2)*t)/\sqrt(\alpha)
u(x, t) = (1/6)*\beta*\sqrt(6)/\sqrt(\alpha)+\sqrt(6)*_C2*cot(_C1+_C2*x+(-2*_C2^3+(1/6)*\beta^2*_C2)*t)/\sqrt(\alpha)
u(x, t) = (1/6)*\beta*\sqrt(6)/\sqrt(\alpha)+\sqrt(6)*_C2*coth(_C1+_C2*x+(2*_C2^3+(1/6)*\beta^2*_C2)*t)/\sqrt(\alpha)
u(x, t) = (1/6)*\beta*\sqrt(6)/\sqrt(\alpha)-\sqrt(6)*_C2*tan(_C1+_C2*x+(-2*_C2^3+(1/6)*\beta^2*_C2)*t)/\sqrt(\alpha)
u(x, t) = (1/6)*\beta*\sqrt(6)/\sqrt(\alpha)+\sqrt(6)*_C2*tanh(_C1+_C2*x+(2*_C2^3+(1/6)*\beta^2*_C2)*t)/\sqrt(\alpha)

行波图[编辑]

Modified KdV-Burgers equation traveling wave plot 1.gif
Modified KdV-Burgers equation traveling wave plot 2.gif
Modified KdV-Burgers equation traveling wave plot 3.gif
Modified KdV-Burgers equation traveling wave plot 4.gif
Modified KdV-Burgers equation traveling wave plot 5.gif
Modified KdV-Burgers equation traveling wave plot 6.gif
Modified KdV-Burgers equation traveling wave plot 7.gif
Modified KdV-Burgers equation traveling wave plot 8.gif


参考文献[编辑]

  1. ^ Andrei D. Polyanin,Valentin F. Zaitsev, HANDBOOK OF NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS, SECOND EDITION p1041 CRC PRESS
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