刘维方程

刘维方程(Liouville equation)是一个非线性偏微分方程：^[1]

${\displaystyle u*u_{xt}-u*u_{x}+\alpha *u^{3}=0}$

解析解

${\displaystyle pu[2]:=ln(-3.4101973587048390836*csc(1.32+1.4934776966447732662*x^{1}.2+1.6440433652163821333*t^{1}.2)^{2})}$ 

${\displaystyle pu[3]:=ln(-3.4101973587048390836*csch(1.32+1.4934776966447732662*x^{1}.2+1.6440433652163821333*t^{1}.2)^{2})}$ 

${\displaystyle pu[4]:=ln(-3.4101973587048390836*sec(1.32+1.4934776966447732662*x^{1}.2+1.6440433652163821333*t^{1}.2)^{2})}$ 

${\displaystyle pu[5]:=ln(3.4101973587048390836*sech(1.32+1.4934776966447732662*x^{1}.2+1.6440433652163821333*t^{1}.2)^{2})}$ 

${\displaystyle pu[9]:=ln(-3.4101973587048390836-3.4101973587048390836*cot(1.32+1.4934776966447732662*x^{1}.2+1.6440433652163821333*t^{1}.2)^{2})}$ 

${\displaystyle pu[12]:=ln(3.4101973587048390836-3.4101973587048390836*tanh(1.32+1.4934776966447732662*x^{1}.2+1.6440433652163821333*t^{1}.2)^{2})}$ 

${\displaystyle pu[13]:=ln(4.1031336303472692620-4.1031336303472692620*coth(1.44+1.6440433652163821333*x^{1}.2+1.7969454312181156991*t^{1}.2)^{2})}$ 

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行波图

Liouville equation traveling wave plot

Liouville equation traveling wave plot

Liouville equation traveling wave plot

Liouville equation traveling wave plot

Liouville equation traveling wave plot

Liouville equation traveling wave plot

Liouville equation traveling wave plot

Liouville equation traveling wave plot

Liouville equation traveling wave plot

参考文献

1. 李志斌编著 《非线性数学物理方程的行波解》105页 科学出版社 2008

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