藤田-斯托姆方程

藤田-斯托姆方程(Fujita-Storm equation)是一个非线性偏微分方程：^[1]

${\displaystyle u_{t}=a*(u^{-2}*u_{x})_{x}}$

解析解

${\displaystyle f1:=1/{\sqrt {(}}2*C1*x-2*a*C1^{2}*t+C2)}$

${\displaystyle f2:=-1/{\sqrt {(}}2*C1*x-2*a*C1^{2}*t+C2)}$

${\displaystyle f3:=1/{\sqrt {(}}(1/2)*C1*(x+C2)^{2}/a+C3*\exp(C1*t))}$

${\displaystyle f4:=-1/{\sqrt {(}}(1/2)*C1*(x+C2)^{2}/a+C3*\exp(C1*t))}$

${\displaystyle f5:=1/({\sqrt {(}}c^{2}*\exp(-2*a*t)+2*\exp(-8*a*t)+2*x*\exp(-4*a*t))*{\sqrt {(}}4-\exp(8*a*t)*(c*\exp(-a*t)+c^{2}*\exp(-2*a*t)+2*\exp(-8*a*t)+2*x*\exp(-4*a*t))))}$

${\displaystyle f6:=1/({\sqrt {(}}c^{2}*\exp(-2*a*t)+2*\exp(-8*a*t)+2*x*\exp(-4*a*t))*{\sqrt {(}}4-\exp(8*a*t)*(c*\exp(-a*t)-c^{2}*\exp(-2*a*t)-2*\exp(-8*a*t)-2*x*\exp(-4*a*t))))}$

${\displaystyle f7:=-1/({\sqrt {(}}c^{2}*\exp(-2*a*t)+2*\exp(-8*a*t)+2*x*\exp(-4*a*t))*{\sqrt {(}}4-\exp(8*a*t)*(c*\exp(-a*t)+c^{2}*\exp(-2*a*t)+2*\exp(-8*a*t)+2*x*\exp(-4*a*t))))}$

${\displaystyle f8:=-1/({\sqrt {(}}c^{2}*\exp(-2*a*t)+2*\exp(-8*a*t)+2*x*\exp(-4*a*t))*{\sqrt {(}}4-\exp(8*a*t)*(c*\exp(-a*t)-c^{2}*\exp(-2*a*t)-2*\exp(-8*a*t)-2*x*\exp(-4*a*t))))}$

${\displaystyle f9:=1/({\sqrt {(}}c^{2}*\exp(2*a*t)+2*\exp(8*a*t)+2*x*\exp(4*a*t))*{\sqrt {(}}\exp(8*a*t)*(c*\exp(-a*t)+c^{2}*\exp(-2*a*t)+2*\exp(-8*a*t)+2*x*\exp(-4*a*t))))}$

${\displaystyle f10:=1/({\sqrt {(}}c^{2}*\exp(2*a*t)+2*\exp(8*a*t)+2*x*\exp(4*a*t))*{\sqrt {(}}\exp(8*a*t)*(c*\exp(-a*t)-c^{2}*\exp(-2*a*t)-2*\exp(-8*a*t)-2*x*\exp(-4*a*t))))}$

${\displaystyle f11:=-1/({\sqrt {(}}c^{2}*\exp(2*a*t)+2*\exp(8*a*t)+2*x*\exp(4*a*t))*{\sqrt {(}}\exp(8*a*t)*(c*\exp(-a*t)+c^{2}*\exp(-2*a*t)+2*\exp(-8*a*t)+2*x*\exp(-4*a*t))))}$

${\displaystyle f12:=-1/({\sqrt {(}}c^{2}*\exp(2*a*t)+2*\exp(8*a*t)+2*x*\exp(4*a*t))*{\sqrt {(}}\exp(8*a*t)*(c*\exp(-a*t)-c^{2}*\exp(-2*a*t)-2*\exp(-8*a*t)-2*x*\exp(-4*a*t))))}$

行波图

藤田-斯托姆方程图

藤田-斯托姆方程图

藤田-斯托姆方程图

藤田-斯托姆方程图

藤田-斯托姆方程图

藤田-斯托姆方程图

藤田-斯托姆方程图

藤田-斯托姆方程图

藤田-斯托姆方程图

藤田-斯托姆方程图

藤田-斯托姆方程图

藤田-斯托姆方程图