radhika

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These are questions asked by radhika

After calculations the integral contains infinity. what it resembles? Is it correct  answer?  Please check the file maple
 

restart

with(DifferentialGeometry):with(JetCalculus):NULL``

DGsetup([x, t], [u], E, 1):

``

 

 
E > 

(-3*t*u[1]^2*u[2]-t*u[2]^3+x*u[1]^3+3*x*u[1]*u[2]^2)*((-2*u[]^2+1)*(-u[1, 1]+u[2, 2])+2*u[]*(-u[1]^2+u[2]^2))/((u[1]-u[2])^3*(u[1]+u[2])^3)

(-3*t*u[1]^2*u[2]-t*u[2]^3+x*u[1]^3+3*x*u[1]*u[2]^2)*((-2*u[]^2+1)*(-u[1, 1]+u[2, 2])+2*u[]*(-u[1]^2+u[2]^2))/((u[1]-u[2])^3*(u[1]+u[2])^3)

(1.1)
E > 

``

E > 

A := evalDG((-3*t*u[1]^2*u[2]-t*u[2]^3+x*u[1]^3+3*x*u[1]*u[2]^2)*((-2*u[]^2+1)*(-u[1, 1]+u[2, 2])+2*u[]*(-u[1]^2+u[2]^2))*`&w`(Dx, Dt)/((u[1]-u[2])^3*(u[1]+u[2])^3))

_DG([["biform", E, [2, 0]], [[[1, 2], -(3*t*u[1]^2*u[2]+t*u[2]^3-x*u[1]^3-3*x*u[1]*u[2]^2)*(2*u[]^2*u[1, 1]-2*u[]^2*u[2, 2]-2*u[]*u[1]^2+2*u[]*u[2]^2-u[1, 1]+u[2, 2])/((u[1]-u[2])^3*(u[1]+u[2])^3)]]])

(1.2)
E > 

simplify(HorizontalHomotopy(A))

_DG([["biform", E, [1, 0]], [[[1], -t*(int(-infinity*(u[1]+u[2])*(1+(u[2, 2]+u[1, 1, 2]+u[1, 2, 2]+u[2]+u[1, 2])*_z1)*_z1*(u[1]-u[2])*(u[1]^4+u[2]^4)*signum(1, (_z1*t*u[2]^6+(-3*_z1*x*u[1]-u[])*u[2]^5+3*_z1*((2/3)*t*u[1]^2+u[]*(t*u[1, 1]+x*u[1, 2]))*u[2]^4-12*(-(1/6)*_z1*x*u[1]^2+(1/6)*u[]*u[1]+_z1*u[]*(t*u[1, 2]+x*u[1, 1]))*u[1]*u[2]^3+18*_z1*u[1]^2*(-(1/6)*t*u[1]^2+u[]*(t*u[1, 1]+x*u[1, 2]))*u[2]^2-12*u[1]^3*(-(1/12)*_z1*x*u[1]^2-(1/4)*u[]*u[1]+_z1*u[]*(t*u[1, 2]+x*u[1, 1]))*u[2]+3*_z1*u[]*u[1]^4*(t*u[1, 1]+x*u[1, 2]))/(_z1^2*(u[1]-u[2])^4*(u[1]+u[2])^4))+infinity*(u[1]+u[2])*_z1*(1+(u[1, 1, 2]+u[1, 2, 2]+u[1]+u[1, 1]+u[1, 2])*_z1)*(u[1]-u[2])*(u[1]^4+u[2]^4)*signum(1, (_z1*x*u[1]^6+(-3*_z1*t*u[2]-u[])*u[1]^5+3*_z1*((2/3)*x*u[2]^2+u[]*(t*u[1, 2]+x*u[2, 2]))*u[1]^4-12*u[2]*(-(1/6)*t*_z1*u[2]^2+(1/6)*u[]*u[2]+_z1*u[]*(t*u[2, 2]+x*u[1, 2]))*u[1]^3+18*_z1*u[2]^2*(-(1/6)*x*u[2]^2+u[]*(t*u[1, 2]+x*u[2, 2]))*u[1]^2-12*(-(1/12)*t*_z1*u[2]^2-(1/4)*u[]*u[2]+_z1*u[]*(t*u[2, 2]+x*u[1, 2]))*u[2]^3*u[1]+3*_z1*u[]*u[2]^4*(t*u[1, 2]+x*u[2, 2]))/(_z1^2*(u[1]-u[2])^4*(u[1]+u[2])^4))+6*(u[]*(u[1]^2-u[2]^2+u[]*(-u[1, 1]+u[2, 2]))*_z1^2-(1/2)*u[2, 2]+(1/2)*u[1, 1])*(t*u[1]^2*u[2]+(1/3)*t*u[2]^3-(1/3)*x*u[1]^3-x*u[1]*u[2]^2), _z1 = 0 .. 1))/((u[1]-u[2])^3*(u[1]+u[2])^3)-signum((t*u[2]^6+(-3*x*u[1]-u[])*u[2]^5+(2*t*u[1]^2+3*u[]*(t*u[1, 1]+x*u[1, 2]))*u[2]^4+(2*x*u[1]^3-2*u[]*u[1]^2-12*u[]*(t*u[1, 2]+x*u[1, 1])*u[1])*u[2]^3+18*(-(1/6)*t*u[1]^2+u[]*(t*u[1, 1]+x*u[1, 2]))*u[1]^2*u[2]^2+(x*u[1]^5+3*u[]*u[1]^4-12*u[]*(t*u[1, 2]+x*u[1, 1])*u[1]^3)*u[2]+3*u[]*u[1]^4*(t*u[1, 1]+x*u[1, 2]))/((u[1]-u[2])^4*(u[1]+u[2])^4))*infinity], [[2], x*(int(-infinity*(u[1]+u[2])*(1+(u[2, 2]+u[1, 1, 2]+u[1, 2, 2]+u[2]+u[1, 2])*_z1)*_z1*(u[1]-u[2])*(u[1]^4+u[2]^4)*signum(1, (_z1*t*u[2]^6+(-3*_z1*x*u[1]-u[])*u[2]^5+3*_z1*((2/3)*t*u[1]^2+u[]*(t*u[1, 1]+x*u[1, 2]))*u[2]^4-12*(-(1/6)*_z1*x*u[1]^2+(1/6)*u[]*u[1]+_z1*u[]*(t*u[1, 2]+x*u[1, 1]))*u[1]*u[2]^3+18*_z1*u[1]^2*(-(1/6)*t*u[1]^2+u[]*(t*u[1, 1]+x*u[1, 2]))*u[2]^2-12*u[1]^3*(-(1/12)*_z1*x*u[1]^2-(1/4)*u[]*u[1]+_z1*u[]*(t*u[1, 2]+x*u[1, 1]))*u[2]+3*_z1*u[]*u[1]^4*(t*u[1, 1]+x*u[1, 2]))/(_z1^2*(u[1]-u[2])^4*(u[1]+u[2])^4))+infinity*(u[1]+u[2])*_z1*(1+(u[1, 1, 2]+u[1, 2, 2]+u[1]+u[1, 1]+u[1, 2])*_z1)*(u[1]-u[2])*(u[1]^4+u[2]^4)*signum(1, (_z1*x*u[1]^6+(-3*_z1*t*u[2]-u[])*u[1]^5+3*_z1*((2/3)*x*u[2]^2+u[]*(t*u[1, 2]+x*u[2, 2]))*u[1]^4-12*u[2]*(-(1/6)*t*_z1*u[2]^2+(1/6)*u[]*u[2]+_z1*u[]*(t*u[2, 2]+x*u[1, 2]))*u[1]^3+18*_z1*u[2]^2*(-(1/6)*x*u[2]^2+u[]*(t*u[1, 2]+x*u[2, 2]))*u[1]^2-12*(-(1/12)*t*_z1*u[2]^2-(1/4)*u[]*u[2]+_z1*u[]*(t*u[2, 2]+x*u[1, 2]))*u[2]^3*u[1]+3*_z1*u[]*u[2]^4*(t*u[1, 2]+x*u[2, 2]))/(_z1^2*(u[1]-u[2])^4*(u[1]+u[2])^4))+6*(u[]*(u[1]^2-u[2]^2+u[]*(-u[1, 1]+u[2, 2]))*_z1^2-(1/2)*u[2, 2]+(1/2)*u[1, 1])*(t*u[1]^2*u[2]+(1/3)*t*u[2]^3-(1/3)*x*u[1]^3-x*u[1]*u[2]^2), _z1 = 0 .. 1))/((u[1]-u[2])^3*(u[1]+u[2])^3)-signum((x*u[1]^6+(-3*t*u[2]-u[])*u[1]^5+(2*x*u[2]^2+3*u[]*(t*u[1, 2]+x*u[2, 2]))*u[1]^4+(2*t*u[2]^3-2*u[]*u[2]^2-12*u[]*(t*u[2, 2]+x*u[1, 2])*u[2])*u[1]^3+18*(-(1/6)*x*u[2]^2+u[]*(t*u[1, 2]+x*u[2, 2]))*u[2]^2*u[1]^2+(t*u[2]^5+3*u[]*u[2]^4-12*u[]*(t*u[2, 2]+x*u[1, 2])*u[2]^3)*u[1]+3*u[]*(t*u[1, 2]+x*u[2, 2])*u[2]^4)/((u[1]-u[2])^4*(u[1]+u[2])^4))*infinity]]])

(1.3)
E > 

``

``

E > 

``

E > 

``


 

Download maple1.mw

1.mw maple1.pdf

Can we use this euler lagrange command for the system of pde's?

If we have a system without lagrangian then euler opertor is applied corresponding to three dependent variables.

so we have three equations but in this euler lagrange command no dependent variable is mentioned.   

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please see the attached pdf.multiplier.pdfmultiplier.pdf

How to convert maple file into the pdf file?For example the attacahed file is maple file.I want to convert this to a pdf file.

conservation_of_wave_eq.mw

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I have tried many times but I didn't get.

 

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