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非线性偏微分方程

亨特 - 萨克斯顿方程编辑

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:

 

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编辑

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]);

 

>f2 := op(TWS[2])

 

> f3 := op(TWS[3]);  

> 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);

 
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);

 
Hunter Saxton equation travelling wave solution3 with Maple TWSolution package