查看“︁Maple/非线性偏微分方程”︁的源代码

'''非线性偏微分方程'''

==亨特 - 萨克斯顿方程==

'''亨特 - 萨克斯顿方程'''(Hunter–Saxton equation)是一个模拟向列型液晶中波动传播的非线性偏微分方程：

:<math>
(u_t + u u_x)_x = \frac{1}{2} \, u_x^2
</math>
以下是利用Maple的软件包TWSolution求亨特 - 萨克斯顿方程的行波解
===Maple TWSolution===
restart;with(PDEtools, TWSolutions, declare):
sys := {diff(u(x, t), x, t)+(diff(u(x, t), x))^2+u(x, t)*(diff(u(x, t), x, x)) = (1/2)*(diff(u(x, t), x))^2}:
> 
> TWS := TWSolutions(sys, extended);
> 
> 
> _C1 := 1.2; _C3 := 2.3; _C4 := .88; _C5 := 1.5; _C2 := .88;

> f1 := op(TWS[1]);

<math>f1 := u(x, t) = -1.7045454545454545454+1.1363636363636363636*(-(1/4)*(6.336*ln(tanh(2.3+.88*x+1.5*t)-1)-6.336*ln(tanh(2.3+.88*x+1.5*t)+1)+9.2928)^(1/3)-(1/4*I)*sqrt(3)*(6.336*ln(tanh(2.3+.88*x+1.5*t)-1)-6.336*ln(tanh(2.3+.88*x+1.5*t)+1)+9.2928)^(1/3))^2</math>

>f2 := op(TWS[2])

<math>f2 := u(x, t) = -1.7045454545454545454+1.1363636363636363636*(-(1/4)*(6.336*ln(tanh(2.3+.88*x+1.5*t)-1)-6.336*ln(tanh(2.3+.88*x+1.5*t)+1)+9.2928)^(1/3)+(1/4*I)*sqrt(3)*(6.336*ln(tanh(2.3+.88*x+1.5*t)-1)-6.336*ln(tanh(2.3+.88*x+1.5*t)+1)+9.2928)^(1/3))^2</math>

> f3 := op(TWS[3]);
<math>u(x, t) = -1.7045454545454545454 + 0.28409090909090909090 (6.336 
  ln(tanh(2.3 + 0.88 x + 1.5 t) - 1)   - 6.336 ln(tanh(2.3 + 0.88 x + 1.5 t) + 1) + 9.2928)^(2/3)</math>

> with(plots);

> animate(complexplot3d, [f[1], x = -15-I .. 15+I, title = "Hunter Saxton  nlpde animation", titlefont = [TIMES, ROMAN, 18], labels = [x, "", ""]], t = 0 .. 30);
[[File:TWS Hunter Saxton animation1.gif|thumb|center|300px|Hunter Saxton equation Maple TWSolution travelling wave solution1]]

> animate(complexplot3d, [f[2], x = -15-I .. 15+I, title = "Hunter Saxton  nlpde animation", titlefont = [TIMES, ROMAN, 18], labels = [x, "", ""]], t = 0 .. 30);



> animate(complexplot3d, [f[3], x = -15-I .. 15+I, title = "Hunter Saxton  nlpde animation", titlefont = [TIMES, ROMAN, 18], labels = [x, "", ""]], t = 0 .. 30);
[[File:TWS Hunter Saxton travelling wave animation3.gif|thumb|center|300px|Hunter Saxton equation travelling wave solution3 with Maple TWSolution package]]