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salim-barzani

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How about upload code...

salim-barzani 1585
December 29 2024
0 0

@dharr it is easy to find all case really is a good code  @ mmcdara write the code i asked letter  for change to arbitrary parameter but he didn't response ,becuase i think  my PDE is not going to zero becuase all parameter there must be a problem i should found i am stuck becuase my pde which i transformed to ode is not going to zero have a problem with parameter but i don't know what is it no one answered untill now i think thus parameter make a problem

A secret...

salim-barzani 1585
December 29 2024
0 0

@janhardo have a long story 

if have any other question ask...

salim-barzani 1585
December 29 2024
0 0

@nm  i try to explain in this file 


 

> 

restart
> 

with(PDEtools)
> 

with(LinearAlgebra)
> 

with(Physics)
> 

with(SolveTools)
> 

undeclare(prime)

`There is no more prime differentiation variable; all derivatives will be displayed as indexed functions`

 (1)
> 

_local(gamma)

Warning, A new binding for the name `gamma` has been created. The global instance of this name is still accessible using the :- prefix, :-`gamma`.  See ?protect for details.

  
> 

declare(Omega(x, t)); declare(U(xi)); declare(u(x, y, z, t)); declare(Q(xi)); declare(V(xi))

Omega(x, t)*`will now be displayed as`*Omega

  

U(xi)*`will now be displayed as`*U

  

u(x, y, z, t)*`will now be displayed as`*u

  

Q(xi)*`will now be displayed as`*Q

  

V(xi)*`will now be displayed as`*V

 (2)
> 

pde1 := I*(diff(Omega(x, t)^m, t))+alpha*(diff(Omega(x, t)^m, `$`(x, 2)))+I*beta*(diff(abs(Omega(x, t))^(2*n)*Omega(x, t)^m, x))+m*sigma*Omega(x, t)^m*(diff(W(t), t)) = I*gamma*abs(Omega(x, t))^(2*n)*(diff(Omega(x, t)^m, x))+delta*abs(Omega(x, t))^(4*n)*Omega(x, t)^m

I*Omega(x, t)^m*m*(diff(Omega(x, t), t))/Omega(x, t)+alpha*(Omega(x, t)^m*m^2*(diff(Omega(x, t), x))^2/Omega(x, t)^2+Omega(x, t)^m*m*(diff(diff(Omega(x, t), x), x))/Omega(x, t)-Omega(x, t)^m*m*(diff(Omega(x, t), x))^2/Omega(x, t)^2)+I*beta*(abs(Omega(x, t))^(2*n)*n*((diff(Omega(x, t), x))*conjugate(Omega(x, t))+Omega(x, t)*(diff(conjugate(Omega(x, t)), x)))*Omega(x, t)^m/abs(Omega(x, t))^2+abs(Omega(x, t))^(2*n)*Omega(x, t)^m*m*(diff(Omega(x, t), x))/Omega(x, t))+m*sigma*Omega(x, t)^m*(diff(W(t), t)) = I*gamma*abs(Omega(x, t))^(2*n)*Omega(x, t)^m*m*(diff(Omega(x, t), x))/Omega(x, t)+delta*abs(Omega(x, t))^(4*n)*Omega(x, t)^m

 (3)
> 

NULL
> 

ode := 4*V(xi)^4*n^2*sigma+(-4*beta*k*m*n^2+4*gamma*k*m*n^2)*V(xi)^3+(4*alpha*k^2*m^2*n^2-4*delta^2*m*n^2+4*m*n^2*w)*V(xi)^2-2*V(xi)*(diff(diff(V(xi), xi), xi))*alpha*m*n+(-alpha*m^2+2*alpha*m*n)*(diff(V(xi), xi))^2 = 0

4*V(xi)^4*n^2*sigma+(-4*beta*k*m*n^2+4*gamma*k*m*n^2)*V(xi)^3+(4*alpha*k^2*m^2*n^2-4*delta^2*m*n^2+4*m*n^2*w)*V(xi)^2-2*V(xi)*(diff(diff(V(xi), xi), xi))*alpha*m*n+(-alpha*m^2+2*alpha*m*n)*(diff(V(xi), xi))^2 = 0

 (4)
> 

L := Omega(x, t) = U(xi)*exp(I*(-k*(tau*c[0]+xi)+w*tau+delta*W(tau)-delta^2*tau))

Omega(x, t) = U(xi)*exp(I*(-k*(tau*c[0]+xi)+w*tau+delta*W(tau)-delta^2*tau))

 (5)
> 

T := U(xi) = V(xi)^(1/(2*n))

U(xi) = V(xi)^((1/2)/n)

 (6)
> 

NULL
> 

ode1 := U(xi)^3*U(xi)^(-1+2*n)*beta*k*m-U(xi)^2*gamma*U(xi)^(2*n)*k*m+U(xi)^2*delta^2*m+I*U(xi)^2*(diff(U(xi), xi))*U(xi)^(-1+2*n)*beta*m-I*U(xi)*(diff(U(xi), xi))*gamma*U(xi)^(2*n)*m-(2*I)*U(xi)*(diff(U(xi), xi))*alpha*k*m^2-U(xi)^2*alpha*k^2*m^2-U(xi)^2*m*w-I*U(xi)*(diff(U(xi), xi))*m*c[0]+(2*I)*U(xi)^2*(diff(U(xi), xi))*U(xi)^(-1+2*n)*beta*n+(diff(U(xi), xi))^2*alpha*m^2-sigma*U(xi)^(4*n)*U(xi)^2+U(xi)*(diff(diff(U(xi), xi), xi))*alpha*m-(diff(U(xi), xi))^2*alpha*m = 0

U(xi)^3*U(xi)^(-1+2*n)*beta*k*m-U(xi)^2*gamma*U(xi)^(2*n)*k*m+U(xi)^2*delta^2*m+I*U(xi)^2*(diff(U(xi), xi))*U(xi)^(-1+2*n)*beta*m-I*U(xi)*(diff(U(xi), xi))*gamma*U(xi)^(2*n)*m-(2*I)*U(xi)*(diff(U(xi), xi))*alpha*k*m^2-U(xi)^2*alpha*k^2*m^2-U(xi)^2*m*w-I*U(xi)*(diff(U(xi), xi))*m*c[0]+(2*I)*U(xi)^2*(diff(U(xi), xi))*U(xi)^(-1+2*n)*beta*n+(diff(U(xi), xi))^2*alpha*m^2-sigma*U(xi)^(4*n)*U(xi)^2+U(xi)*(diff(diff(U(xi), xi), xi))*alpha*m-(diff(U(xi), xi))^2*alpha*m = 0

 (7)
> 

S := diff(G(xi), `$`(xi, 2))+(2*m*mu+lambda)*(diff(G(xi), xi))+mu = 0

diff(diff(G(xi), xi), xi)+(2*m*mu+lambda)*(diff(G(xi), xi))+mu = 0

 (8)
> 

S1 := dsolve(S, G(xi))

G(xi) = -exp(-(2*m*mu+lambda)*xi)*c__1/(2*m*mu+lambda)-mu*xi/(2*m*mu+lambda)+c__2

 (9)
> 

S2 := diff(G(xi) = -exp(-(2*m*mu+lambda)*xi)*c__1/(2*m*mu+lambda)-mu*xi/(2*m*mu+lambda)+c__2, xi)

diff(G(xi), xi) = -(-2*m*mu-lambda)*exp(-(2*m*mu+lambda)*xi)*c__1/(2*m*mu+lambda)-mu/(2*m*mu+lambda)

 (10)
> 

K := V(xi) = a[-1]/(m+1/(diff(G(xi), xi)))+a[0]+a[1]*(m+1/(diff(G(xi), xi)))

V(xi) = a[-1]/(m+1/(diff(G(xi), xi)))+a[0]+a[1]*(m+1/(diff(G(xi), xi)))

 (11)
> 

case1 := {alpha = alpha, beta = gamma, delta = delta, gamma = gamma, k = k, lambda = 0, m = 2*n, mu = mu, n = n, sigma = 32*alpha*mu^2*n^4/a[-1]^2, w = -2*alpha*k^2*n-4*alpha*mu^2*n+delta^2, a[-1] = a[-1], a[0] = 0, a[1] = 0}

{alpha = alpha, beta = gamma, delta = delta, gamma = gamma, k = k, lambda = 0, m = 2*n, mu = mu, n = n, sigma = 32*alpha*mu^2*n^4/a[-1]^2, w = -2*alpha*k^2*n-4*alpha*mu^2*n+delta^2, a[-1] = a[-1], a[0] = 0, a[1] = 0}

 (12)
> 

F1 := subs(case1, K)

V(xi) = a[-1]/(2*n+1/(diff(G(xi), xi)))

 (13)
> 

F2 := subs(case1, ode)

128*V(xi)^4*n^6*alpha*mu^2/a[-1]^2+(16*alpha*k^2*n^4-8*delta^2*n^3+8*n^3*(-2*alpha*k^2*n-4*alpha*mu^2*n+delta^2))*V(xi)^2-4*V(xi)*(diff(diff(V(xi), xi), xi))*alpha*n^2 = 0

 (14)

``

 (15)
> 

W1 := subs(S2, F1)

V(xi) = a[-1]/(2*n+1/(-(-2*m*mu-lambda)*exp(-(2*m*mu+lambda)*xi)*c__1/(2*m*mu+lambda)-mu/(2*m*mu+lambda)))

 (16)
> 

W2 := subs(case1, W1)

V(xi) = a[-1]/(2*n+1/(exp(-4*mu*n*xi)*c__1-(1/4)/n))

 (17)
> 

odetest(W2, F2)

0

 (18)
> 

NULL
> 

NULL
> 

T2 := subs(W2, T)

U(xi) = (a[-1]/(2*n+1/(exp(-4*mu*n*xi)*c__1-(1/4)/n)))^((1/2)/n)

 (19)
> 

T3 := subs(T2, L)

Omega(x, t) = (a[-1]/(2*n+1/(exp(-4*mu*n*xi)*c__1-(1/4)/n)))^((1/2)/n)*exp(I*(-k*(tau*c[0]+xi)+w*tau+delta*W(tau)-delta^2*tau))

 (20)
> 

condition1 := c[0] = -2*alpha*k*m; condition2 := beta = gamma*m/(m+2*n)

c[0] = -2*alpha*k*m

  

beta = gamma*m/(m+2*n)

 (21)
> 

n := 2; M := 1

2

  

1

 (22)
> 

P := subs(case1, ode1)

4*U(xi)^2*delta^2-(32*I)*U(xi)*(diff(U(xi), xi))*alpha*k-16*U(xi)^2*alpha*k^2-4*U(xi)^2*(-4*alpha*k^2-8*alpha*mu^2+delta^2)-(4*I)*U(xi)*(diff(U(xi), xi))*c[0]+(4*I)*U(xi)^5*(diff(U(xi), xi))*gamma+12*(diff(U(xi), xi))^2*alpha-512*alpha*mu^2*U(xi)^10/a[-1]^2+4*U(xi)*(diff(diff(U(xi), xi), xi))*alpha = 0

 (23)
> 

P1 := subs(case1, T2)

U(xi) = (a[-1]/(4+1/(exp(-8*mu*xi)*c__1-1/8)))^(1/4)

 (24)
> 

Pe := odetest(P1, P)

-(512*I)*mu*c__1*(8*c__1*a[-1]/(exp(8*mu*xi)+8*c__1)-a[-1]*exp(8*mu*xi)/(exp(8*mu*xi)+8*c__1))^(1/2)*exp(16*mu*xi)*alpha*k/((exp(8*mu*xi)-8*c__1)*(exp(8*mu*xi)+8*c__1)^2)-(16*I)*mu*c__1*(8*c__1*a[-1]/(exp(8*mu*xi)+8*c__1)-a[-1]*exp(8*mu*xi)/(exp(8*mu*xi)+8*c__1))^(1/2)*exp(16*mu*xi)*gamma*a[-1]/((exp(8*mu*xi)-8*c__1)*(exp(8*mu*xi)+8*c__1)^2)-(4096*I)*mu*c__1^2*(8*c__1*a[-1]/(exp(8*mu*xi)+8*c__1)-a[-1]*exp(8*mu*xi)/(exp(8*mu*xi)+8*c__1))^(1/2)*exp(8*mu*xi)*alpha*k/((exp(8*mu*xi)-8*c__1)*(exp(8*mu*xi)+8*c__1)^2)+(128*I)*mu*c__1^2*(8*c__1*a[-1]/(exp(8*mu*xi)+8*c__1)-a[-1]*exp(8*mu*xi)/(exp(8*mu*xi)+8*c__1))^(1/2)*exp(8*mu*xi)*gamma*a[-1]/((exp(8*mu*xi)-8*c__1)*(exp(8*mu*xi)+8*c__1)^2)-(64*I)*mu*c__1*(8*c__1*a[-1]/(exp(8*mu*xi)+8*c__1)-a[-1]*exp(8*mu*xi)/(exp(8*mu*xi)+8*c__1))^(1/2)*exp(16*mu*xi)*c[0]/((exp(8*mu*xi)-8*c__1)*(exp(8*mu*xi)+8*c__1)^2)-(512*I)*mu*c__1^2*(8*c__1*a[-1]/(exp(8*mu*xi)+8*c__1)-a[-1]*exp(8*mu*xi)/(exp(8*mu*xi)+8*c__1))^(1/2)*exp(8*mu*xi)*c[0]/((exp(8*mu*xi)-8*c__1)*(exp(8*mu*xi)+8*c__1)^2)

 (25)
> 

subs({condition1, condition2}, Pe)

-(512*I)*mu*c__1*(8*c__1*a[-1]/(exp(8*mu*xi)+8*c__1)-a[-1]*exp(8*mu*xi)/(exp(8*mu*xi)+8*c__1))^(1/2)*exp(16*mu*xi)*alpha*k/((exp(8*mu*xi)-8*c__1)*(exp(8*mu*xi)+8*c__1)^2)-(16*I)*mu*c__1*(8*c__1*a[-1]/(exp(8*mu*xi)+8*c__1)-a[-1]*exp(8*mu*xi)/(exp(8*mu*xi)+8*c__1))^(1/2)*exp(16*mu*xi)*gamma*a[-1]/((exp(8*mu*xi)-8*c__1)*(exp(8*mu*xi)+8*c__1)^2)-(4096*I)*mu*c__1^2*(8*c__1*a[-1]/(exp(8*mu*xi)+8*c__1)-a[-1]*exp(8*mu*xi)/(exp(8*mu*xi)+8*c__1))^(1/2)*exp(8*mu*xi)*alpha*k/((exp(8*mu*xi)-8*c__1)*(exp(8*mu*xi)+8*c__1)^2)+(128*I)*mu*c__1^2*(8*c__1*a[-1]/(exp(8*mu*xi)+8*c__1)-a[-1]*exp(8*mu*xi)/(exp(8*mu*xi)+8*c__1))^(1/2)*exp(8*mu*xi)*gamma*a[-1]/((exp(8*mu*xi)-8*c__1)*(exp(8*mu*xi)+8*c__1)^2)+(128*I)*mu*c__1*(8*c__1*a[-1]/(exp(8*mu*xi)+8*c__1)-a[-1]*exp(8*mu*xi)/(exp(8*mu*xi)+8*c__1))^(1/2)*exp(16*mu*xi)*alpha*k*m/((exp(8*mu*xi)-8*c__1)*(exp(8*mu*xi)+8*c__1)^2)+(1024*I)*mu*c__1^2*(8*c__1*a[-1]/(exp(8*mu*xi)+8*c__1)-a[-1]*exp(8*mu*xi)/(exp(8*mu*xi)+8*c__1))^(1/2)*exp(8*mu*xi)*alpha*k*m/((exp(8*mu*xi)-8*c__1)*(exp(8*mu*xi)+8*c__1)^2)

 (26)
> 

NULL
> 

NULL

NULL


 

Download explain.mw

a question?...

salim-barzani 1585
December 28 2024
0 0

@mmcdara  in the code i don't want all parameter maybe 4 or 5 is enough How i do that?

F-P.mw

thank you so much...

salim-barzani 1585
December 28 2024
0 0

@acer  last night my work stoped becuase of this physic i will not used anymore untill i something strange appear.

nothing,...

salim-barzani 1585
December 27 2024
0 0

@acer  just some time  a new sign appear with physic they remove , why problem is physic?

i like your code style...

salim-barzani 1585
December 27 2024
0 0

@mmcdara is different no one can undrestand except you  best of best thank you so much.

Thanks you, you did a great job...

salim-barzani 1585
December 27 2024
0 0

@mmcdara you are legend of the coding

How you did that?...

salim-barzani 1585
December 27 2024
0 0

@mmcdara  i look to my old code and find another thing but is not give my answer even 

How you do that is unbliavable , just this is unclear for me why the author just write a[-1],a[1],c[4] 

> 

restart
> 

with(PDEtools)
> 

with(LinearAlgebra)
> 

NULL
> 

with(SolveTools)
> 

undeclare(prime)

`There is no more prime differentiation variable; all derivatives will be displayed as indexed functions`

 (1)
> 

lprint

lprint

 (2)
> 

declare(Omega(x, t)); declare(U(xi)); declare(u(x, y, z, t)); declare(Q(xi))

Omega(x, t)*`will now be displayed as`*Omega

  

U(xi)*`will now be displayed as`*U

  

u(x, y, z, t)*`will now be displayed as`*u

  

Q(xi)*`will now be displayed as`*Q

 (3)
> 

tr := {t = tau, x = (-ZETA*c[3]-tau*c[4]-`Υ`*c[2]+xi)/c[1], y = `Υ`, z = ZETA, u(x, y, z, t) = U(xi)}
> 

pde1 := diff(u(x, y, z, t), `$`(x, 3), z)-4*(diff(u(x, y, z, t), x, t))+4*(diff(u(x, y, z, t), x))*(diff(u(x, y, z, t), x, z))+2*(diff(u(x, y, z, t), `$`(x, 2)))*(diff(u(x, y, z, t), z))+3*(diff(u(x, y, z, t), `$`(y, 2))) = 0
> 

``
> 

L1 := PDEtools:-dchange(tr, pde1, [xi, `Υ`, ZETA, tau, U])
> 

map(int, L1, xi)
> 

ode := %
> 

F := sum(a[i]*(m+1/(diff(G(xi), xi)))^i, i = -1 .. 1)
> 

D1 := diff(F, xi)
> 

S := diff(G(xi), `$`(xi, 2)) = -(2*m*mu+lambda)*(diff(G(xi), xi))-mu
> 

E1 := subs(S, D1)
> 

D2 := diff(E1, xi)
> 

E2 := subs(S, D2)
> 

D3 := diff(E2, xi)
> 

E3 := subs(S, D3)
> 

NULL
> 

NULL
> 

K := U(xi) = F
> 

K1 := diff(U(xi), xi) = E1
> 

K2 := diff(U(xi), `$`(xi, 2)) = E2
> 

K3 := diff(U(xi), `$`(xi, 3)) = E3
> 

NULL
> 

L := eval(ode, {K, K1, K2, K3})

c[1]^3*c[3]*(6*a[-1]*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)^3/((m+1/(diff(G(xi), xi)))^4*(diff(G(xi), xi))^6)-12*a[-1]*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)^3/((m+1/(diff(G(xi), xi)))^3*(diff(G(xi), xi))^5)-6*a[-1]*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)^2*(2*m*mu+lambda)/((m+1/(diff(G(xi), xi)))^3*(diff(G(xi), xi))^4)+6*a[-1]*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)^3/((m+1/(diff(G(xi), xi)))^2*(diff(G(xi), xi))^4)+6*a[-1]*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)^2*(2*m*mu+lambda)/((m+1/(diff(G(xi), xi)))^2*(diff(G(xi), xi))^3)+a[-1]*(2*m*mu+lambda)^2*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)/((m+1/(diff(G(xi), xi)))^2*(diff(G(xi), xi))^2)-6*a[1]*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)^3/(diff(G(xi), xi))^4-6*a[1]*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)^2*(2*m*mu+lambda)/(diff(G(xi), xi))^3-a[1]*(2*m*mu+lambda)^2*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)/(diff(G(xi), xi))^2)+3*c[2]^2*(a[-1]*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)/((m+1/(diff(G(xi), xi)))^2*(diff(G(xi), xi))^2)-a[1]*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)/(diff(G(xi), xi))^2)-4*c[4]*c[1]*(a[-1]*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)/((m+1/(diff(G(xi), xi)))^2*(diff(G(xi), xi))^2)-a[1]*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)/(diff(G(xi), xi))^2)+3*c[1]^2*c[3]*(a[-1]*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)/((m+1/(diff(G(xi), xi)))^2*(diff(G(xi), xi))^2)-a[1]*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)/(diff(G(xi), xi))^2)^2 = 0

 (4)
> 

NULL
> 

# rewritting rule

RR := isolate(m+1/(diff(G(xi), xi))=Phi, diff(G(xi), xi));

diff(G(xi), xi) = 1/(Phi-m)

 (5)
> 

# Apply RR and collect wrt Phi

subs(RR, L):
normal(%):
PhiN := collect(numer(lhs(%)), Phi):
PhiD := denom(lhs(%%));

Phi^4

 (6)
> 



with(LargeExpressions):

LLE := collect(PhiN, Phi, Veil[phi] ):
LLE / PhiD = 0;

(3*Phi^8*phi[1]+6*Phi^7*phi[2]+Phi^6*phi[3]+Phi^5*phi[4]-Phi^4*phi[5]-Phi^3*phi[6]+Phi^2*phi[7]-6*Phi*phi[8]+3*phi[9])/Phi^4 = 0

 (7)
> 

# phi[i] coefficients

CoefficientNullity:=print~( [ seq( phi[i] = simplify(Unveil[phi](phi[i]), size), i=1..LastUsed[phi] ) ] ):

phi[1] = mu^2*a[1]*c[1]^2*c[3]*(2*mu*c[1]+a[1])

  

phi[2] = lambda*mu*a[1]*c[1]^2*c[3]*(2*mu*c[1]+a[1])

  

phi[3] = -8*(mu*c[3]*(m^2*mu^2+m*mu*lambda-(7/8)*lambda^2)*c[1]^3+(3/4)*c[3]*((m^2*a[1]+a[-1])*mu^2+m*mu*lambda*a[1]-(1/2)*lambda^2*a[1])*c[1]^2+(1/2)*mu*c[1]*c[4]-(3/8)*mu*c[2]^2)*a[1]

  

phi[4] = -8*lambda*(c[3]*(m^2*mu^2+m*mu*lambda-(1/8)*lambda^2)*c[1]^3+(3/4)*(m*lambda*a[1]+mu*(m^2*a[1]+2*a[-1]))*c[3]*c[1]^2+(1/2)*c[1]*c[4]-(3/8)*c[2]^2)*a[1]

  

phi[5] = -2*(m^2*mu^2+m*mu*lambda-(1/2)*lambda^2)*((m^2*a[1]+a[-1])*mu+m*lambda*a[1])*c[3]*c[1]^3-3*((m^4*a[1]^2+4*m^2*a[-1]*a[1]+a[-1]^2)*mu^2+2*m*lambda*a[1]*(m^2*a[1]+2*a[-1])*mu+lambda^2*a[1]*(m^2*a[1]-2*a[-1]))*c[3]*c[1]^2-4*c[4]*((m^2*a[1]+a[-1])*mu+m*lambda*a[1])*c[1]+3*c[2]^2*((m^2*a[1]+a[-1])*mu+m*lambda*a[1])

  

phi[6] = -8*a[-1]*(c[3]*(m^2*mu^2+m*mu*lambda-(1/8)*lambda^2)*c[1]^3+(3/2)*(m*lambda*a[1]+mu*(m^2*a[1]+(1/2)*a[-1]))*c[3]*c[1]^2+(1/2)*c[1]*c[4]-(3/8)*c[2]^2)*lambda

  

phi[7] = -8*a[-1]*(mu^2*c[1]^2*c[3]*(mu*c[1]+(3/4)*a[1])*m^4+2*mu*lambda*c[1]^2*c[3]*(mu*c[1]+(3/4)*a[1])*m^3+((1/8)*mu*c[3]*c[1]^3*lambda^2+(3/4)*c[3]*(lambda^2*a[1]+mu^2*a[-1])*c[1]^2+(1/2)*mu*c[1]*c[4]-(3/8)*mu*c[2]^2)*m^2+(3/4)*lambda*(-(7/6)*c[1]^3*c[3]*lambda^2+mu*a[-1]*c[1]^2*c[3]+(2/3)*c[1]*c[4]-(1/2)*c[2]^2)*m-(3/8)*lambda^2*a[-1]*c[1]^2*c[3])

  

phi[8] = a[-1]*lambda*c[3]*(m*mu+lambda)*m*(2*m^2*mu*c[1]+2*lambda*m*c[1]+a[-1])*c[1]^2

  

phi[9] = a[-1]*c[3]*(m*mu+lambda)^2*m^2*(2*m^2*mu*c[1]+2*lambda*m*c[1]+a[-1])*c[1]^2

 (8)
> 

COEFFS := solve({phi[1],phi[2],phi[3],phi[4],phi[5],phi[6],phi[7],phi[8],phi[9]}, {a[-1],a[1],mu,c[4]})

(9)
> 

C := solve({phi[1], phi[2], phi[3], phi[4], phi[5], phi[6], phi[7], phi[8], phi[9]}, {a[-1], a[0], a[1], c[4]})

(10)
> 

sols := solve(CoefficientNullity, [a[-1], a[0], a[1], c[4]]); sols := `assuming`([eval(sols)], [b > 0]); whattype(sols); print(cat(`$`('_', 120))); `~`[print](sols)

[[a[-1] = a[-1], a[0] = a[0], a[1] = a[1], c[4] = c[4]]]

  

list

  

________________________________________________________________________________________________________________________

  

[a[-1] = a[-1], a[0] = a[0], a[1] = a[1], c[4] = c[4]]

 (11)
 

 

Download mmcdara-new-M-F-P.mw

don't waste time...

salim-barzani 1585
December 26 2024
0 0

@janhardo they are unchangable 

this is my first time i asked this...

salim-barzani 1585
December 26 2024
0 0

@mmcdara I’m not sure why they did that, and I think I’ve deleted all my previous posts about this because of them also hirota operator. That aside, I thought the graph should look like this in 2D—the middle one. 

question?...

salim-barzani 1585
December 25 2024
0 0

@mmcdara How i can plot 2D of this data? it will show effect of noise?

reply...

salim-barzani 1585
December 25 2024
0 0

@mmcdara 

Thank you so much for providing the code and for your effort! I truly appreciate your help. I have a few questions regarding the implementation:

  1. What happens to the W(t)W(t)W(t) function in the code? You’ve initialized it as w(t)=0w(t) = 0w(t)=0, but is this just the initial condition?

  2. In the line STX := TX_Wfree *~ T_W;, what does this operation mean conceptually?

  3. How can I modify the matrix to include additional data, such as adding a new column?

  4. I’d like to improve the design and visual clarity of the plot directly within the program, without using external tools. I need these plots for my paper and would like to include labels for the axes, specifying whether they represent absolute, real, or imaginary values for each graph. Additionally, is it possible to generate 2D plots for each graph of the STX matrix?

Your assistance is invaluable, and it will significantly enhance my work. I’ll always remember your support and contribution.

 

reply...

salim-barzani 1585
December 25 2024
0 0

@nm  i posted the same in mathematica someone at there answered then i read the paper at one place he mention that . and effect of noise he not shown in graph i don't know what is w(t) at his graph 

reply...

salim-barzani 1585
December 25 2024
0 0

@nm  when epsilon= +&- 1 the answer satisfy

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