LeeHoYeung

Mr. Ho Yeung Lee

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12 years, 235 days

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Seldom to ask question after retired math hobby Welcome August, February, July, May born girl And waited for her email to mavio@protonmail.com

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These are questions asked by LeeHoYeung

c1 := u1*u2-u1*u3;

c2 := -u1*u2+u2*u3-(1/2)*((u2-u3)*(u1*u2-u1*u3)+(u1)*(-u1*u2+u2*u3)-(u1)*(u1*u3-u2*u3))/(u1);

c3 := u1*u3-u2*u3+(1/2)*((u2-u3)*(u1*u2-u1*u3)+(u1)*(-u1*u2+u2*u3)-(u1)*(u1*u3-u2*u3))/(u1);

c4 := u1;

d1 := subs(u3=u3(t),subs(u2=u2(t),subs(u1=u1(t),c1)));

d2 := subs(u3=u3(t),subs(u2=u2(t),subs(u1=u1(t),c2)));

d3 := subs(u3=u3(t),subs(u2=u2(t),subs(u1=u1(t),c3)));

d4 := subs(u3=u3(t),subs(u2=u2(t),subs(u1=u1(t),c4)));

sys := {Diff(u1(t), t) = d1,

Diff(u2(t), t) = d2,

Diff(u3(t), t) = d3,

y = d4};

sys := {Diff(u1(t), t) = d1,

Diff(u2(t), t) = d2,

Diff(u3(t), t) = d3};

with(DEtools):

DEplot(sys, [u1(t), u2(t), u3(t)], t = 0 .. 15,number = 3, [[u1(0) = 0, u2(0) = 0, u3(0) = 0]]);

 

Error, (in DEtools/DEplot/WhichPlot) More than two dependent variables - please indicate the desired scene.

                          

how to find lie group or finite group or symmetry group of one differential equation or system of differential equations

restart;

Lfh := proc(numoflevel, h, fx, var)

if numoflevel = 1 then

        hello := 0;

        for i from 1 to nops(var) do

                hello := hello + diff(h[i], var[i])*fx[i];

        od;

        return hello;

else

        hello := 0;

        for i from 1 to nops(var) do

                hello := hello + diff(Lfh(numoflevel-1, h, fx, var), var[i])*fx[i];

        od;

        return hello;

end if;

end proc:

f:=[x3-x2^3,-x2,x1^2-x3];

g:=[0,-1,1];

h:=[x1,0,0];

variables := [x1,x2,x3];

Lf1h := Lfh(1,h,f,variables);

Lgf1h := Lfh(1,[seq(Lf1h,n=1..nops(variables))],g,variables);

Lf2h := Lfh(2,h,f,variables);

Lgf2h := Lfh(1,[seq(Lf2h,n=1..nops(variables))],g,variables);

Lf3h := Lfh(3,h,f,variables);

Lgf3h := Lfh(1,[seq(Lf3h,n=1..nops(variables))],g,variables);

 

i doubt that my book example is wrong

it said relative rank is 2, but i can not find any zero when Lgf3h

if i continue to Lgf4h, Lgf5h, Lgf6h...etc, still no zero what does it mean?

Example

Diff(x1,t) = x2^2,
Diff(x2,t) = u,
y = x1

result in

Diff(y,t$2)-4*u^2*Diff(y,t) = 0
2*u*x2 - Diff(y,t^2) = 0
x1 - y = 0

is it possible a general and generic method to apply some steps on system below

Diff(u1, t) = u1*u2-u1*u3,
Diff(u2, t) = -u1*u2+u2*u3-(1/2)*(conjugate(u2-u3)*(u1*u2-u1*u3)+conjugate(u1)*(-u1*u2+u2*u3)-conjugate(u1)*(u1*u3-u2*u3))/conjugate(u1),
Diff(u3, t) = u1*u3-u2*u3+(1/2)*(conjugate(u2-u3)*(u1*u2-u1*u3)+conjugate(u1)*(-u1*u2+u2*u3)-conjugate(u1)*(u1*u3-u2*u3))/conjugate(u1),
y = u1

x11 := Vector([0.208408965651696e-3, -0.157194487523421e-2, -0.294739401402979e-2, 0.788206708183853e-2, 0.499394753201753e-2, 0.191468321959759e-3, 0.504980449104750e-2, 0.222150494088535e-2, 0.132091821964287e-2, 0.161118434883258e-2, -0.281236534046873e-2, -0.398055875132037e-2, -0.111753680372819e-1, 0.588868146012489e-2, -0.354191562612469e-2, 0.984082837373291e-3, -0.116041186868374e-1, 0.603027845850267e-3, -0.448778128168742e-2, -0.127561485214862e-1, -0.412027655195339e-2, 0.379387381798949e-2, -0.602550446997765e-2, -0.605986284736216e-2, -0.751396992404410e-2, 0.633613424008655e-2, -0.677581832613623e-2]):
y11 := Vector([ -21321.9719565717, 231.709204951251, 1527.92905167191, -32.8508507060675, 54.9408176234139, -99.4222178124229, -675.771433486265, 42.0838668074923, -12559.3183308951, 5.21412214166344*10^5, 1110.50031772203, 3.67149699000155, -108.543878970269, -8.48861069398811, -521.810552387313, 26.4792411876883, -8.32240296737599, -1085.40982521906, -44.1390030597906, -203.891397612798, -56.3746416571417, -218.205643256096, -178.991498697065, -42.2468018350386, .328546922634921, -1883.18308996621, 111.747881085748]):
z11 := Vector([ 1549.88755331800, -329.861725802688, 8.54200301129155, -283.381775745327, -54.5469129127573, 1875.94875597129, -16.2230517860850, 6084.82381954832, 1146.15489803104, -456.460512914647, 104.533252701641, 16.3998365630734, 11.5710907832054, -175.370276462696, 33.8045539958636, 2029.50029336951, 1387.92643570857, 9.54717543291120, -1999.09590358328, 29.7628085078953, 2.58210333216737*10^6, 57.7969622731082, -6.42551196941394, -8549.23677077892, -49.0081775323244, -72.5156360537114, 183.539911458475]):

 

> seq({round(x11[k]), round(y11[k]), round(z11[k])}, k = 1 .. 27);
{-21322, 0, 1550}, {-330, 0, 232}, {0, 9, 1528}, {-283, -33, 0}, {-55, 0, 55},

{-99, 0, 1876}, {-676, -16, 0}, {0, 42, 6085}, {-12559, 0, 1146},

{-456, 0, 521412}, {0, 105, 1111}, {0, 4, 16}, {-109, 0, 12}, {-175, -8, 0},

{-522, 0, 34}, {0, 26, 2030}, {-8, 0, 1388}, {-1085, 0, 10},

{-1999, -44, 0}, {-204, 0, 30}, {-56, 0, 2582103}, {-218, 0, 58},

{-179, -6, 0}, {-8549, -42, 0}, {-49, 0}, {-1883, -73, 0}, {0, 112, 184}

 

https://drive.google.com/file/d/0B2D69u2pweEvS0RVTFZWTnVKWms/edit?usp=sharing

{-49, 0}

there is a missing comma in this, is it the built in robot in maple playing human or my window make a joke?

 

this bug make me get an misunderstanding from mathematica stackexchange

 

https://drive.google.com/file/d/0B2D69u2pweEvZXp5WndMN0x5VGs/edit?usp=sharing

 

i can not display web correctly, What's wrong with me?

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