salim-barzani

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0 years, 215 days

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These are questions asked by salim-barzani

i want to get zero of this function i did all part true but i don't know why my pde not getting zero after substitute each parameter and part 

restart

with(PDEtools)

NULL

undeclare(prime)

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

(1)

p := 2*k; n := 1; xi := -p*t+x

2*k

 

1

 

-2*k*t+x

(2)

"U(xi):=(B[1] (RootOf(3 _Z^2-3 _Z-1)+coth(xi)))^(-1/n);u(x,t):=(B[1] (RootOf(3 _Z^2-3 _Z-1)+coth(-p t+x)))^(-1/n) (e)^(ⅈ (k x-t w))"

proc (xi) options operator, arrow, function_assign; (B[1]*(RootOf(3*_Z^2-3*_Z-1)+coth(xi)))^(-1/n) end proc

 

proc (x, t) options operator, arrow, function_assign; (B[1]*(RootOf(3*_Z^2-3*_Z-1)+coth(-p*t+x)))^(-1/n)*exp(I*(k*x-t*w)) end proc

(3)

pde := I*(diff(u(x, t), t))+diff(u(x, t), `$`(x, 2))+eta*u(x, t)+beta*U(xi)^n*u(x, t)+gamma*U(xi)^(2*n)*u(x, t)+delta*U(xi)^(3*n)*u(x, t)+lambda*U(xi)^(4*n)*u(x, t) = 0

I*(2*exp(I*(k*x-t*w))*k*(1-coth(2*k*t-x)^2)/(B[1]*(RootOf(3*_Z^2-3*_Z-1)-coth(2*k*t-x))^2)-I*w*exp(I*(k*x-t*w))/(B[1]*(RootOf(3*_Z^2-3*_Z-1)-coth(2*k*t-x))))+2*exp(I*(k*x-t*w))*(1-coth(2*k*t-x)^2)^2/(B[1]*(RootOf(3*_Z^2-3*_Z-1)-coth(2*k*t-x))^3)-(2*I)*k*exp(I*(k*x-t*w))*(1-coth(2*k*t-x)^2)/(B[1]*(RootOf(3*_Z^2-3*_Z-1)-coth(2*k*t-x))^2)+2*exp(I*(k*x-t*w))*coth(2*k*t-x)*(-1+coth(2*k*t-x)^2)/(B[1]*(RootOf(3*_Z^2-3*_Z-1)-coth(2*k*t-x))^2)-k^2*exp(I*(k*x-t*w))/(B[1]*(RootOf(3*_Z^2-3*_Z-1)-coth(2*k*t-x)))+eta*exp(I*(k*x-t*w))/(B[1]*(RootOf(3*_Z^2-3*_Z-1)-coth(2*k*t-x)))+beta*exp(I*(k*x-t*w))/(B[1]^2*(RootOf(3*_Z^2-3*_Z-1)-coth(2*k*t-x))^2)+gamma*exp(I*(k*x-t*w))/(B[1]^3*(RootOf(3*_Z^2-3*_Z-1)-coth(2*k*t-x))^3)+delta*exp(I*(k*x-t*w))/(B[1]^4*(RootOf(3*_Z^2-3*_Z-1)-coth(2*k*t-x))^4)+lambda*exp(I*(k*x-t*w))/(B[1]^5*(RootOf(3*_Z^2-3*_Z-1)-coth(2*k*t-x))^5) = 0

(4)

case1 := [beta = 2*RootOf(3*_Z^2-3*_Z-1)*(n+2)/(B[1]*n^2), delta = 2*B[1]*(RootOf(3*_Z^2-3*_Z-1)+1)*(3*n+2)/(3*n^2), eta = (k^2*n^2*B[1]^2-n^2*w*B[1]^2-1)/(n^2*B[1]^2), gamma = -6*RootOf(3*_Z^2-3*_Z-1)*(n+1)/n^2, lambda = B[1]^2*(3*RootOf(3*_Z^2-3*_Z-1)-7)*(2*n+1)/(9*n^2), A[0] = RootOf(3*_Z^2-3*_Z-1)*B[1], A[1] = 0, B[1] = B[1]]

[beta = 6*RootOf(3*_Z^2-3*_Z-1)/B[1], delta = (10/3)*B[1]*(RootOf(3*_Z^2-3*_Z-1)+1), eta = (k^2*B[1]^2-w*B[1]^2-1)/B[1]^2, gamma = -12*RootOf(3*_Z^2-3*_Z-1), lambda = (1/3)*B[1]^2*(3*RootOf(3*_Z^2-3*_Z-1)-7), A[0] = RootOf(3*_Z^2-3*_Z-1)*B[1], A[1] = 0, B[1] = B[1]]

(5)

pde3 := eval(pde, case1)

 

``

Download test.mw

the second ode is giving me zero also when we back to orginal under the condition by using them must the orginal ode be zero but i don't know where is mistake , when Orginal paper use some thing different but i think they must have same results i don't know i use them wrong i am not sure at here just , when U(xi)=y(z) in my mw

restart

with(PDEtools)

NULL

undeclare(prime)

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

(1)

NULL

G := V(xi) = RootOf(3*_Z^2-3*_Z-1)*B[1]+B[1]*(exp(xi)+exp(-xi))/(exp(xi)-exp(-xi))

V(xi) = RootOf(3*_Z^2-3*_Z-1)*B[1]+B[1]*(exp(xi)+exp(-xi))/(exp(xi)-exp(-xi))

(2)

NULL

p := 2*k

2*k

(3)

ode := I*(-(diff(U(xi), xi))*p*exp(I*(k*x-t*w))-I*U(xi)*w*exp(I*(k*x-t*w)))+(diff(diff(U(xi), xi), xi))*exp(I*(k*x-t*w))+(2*I)*(diff(U(xi), xi))*k*exp(I*(k*x-t*w))-U(xi)*k^2*exp(I*(k*x-t*w))+eta*U(xi)*exp(I*(k*x-t*w))+beta*U(xi)^n*U(xi)*exp(I*(k*x-t*w))+gamma*U(xi)^(2*n)*U(xi)*exp(I*(k*x-t*w))+delta*U(xi)^(3*n)*U(xi)*exp(I*(k*x-t*w))+lambda*U(xi)^(4*n)*U(xi)*exp(I*(k*x-t*w)) = 0

I*(-2*(diff(U(xi), xi))*k*exp(I*(k*x-t*w))-I*U(xi)*w*exp(I*(k*x-t*w)))+(diff(diff(U(xi), xi), xi))*exp(I*(k*x-t*w))+(2*I)*(diff(U(xi), xi))*k*exp(I*(k*x-t*w))-U(xi)*k^2*exp(I*(k*x-t*w))+eta*U(xi)*exp(I*(k*x-t*w))+beta*U(xi)^n*U(xi)*exp(I*(k*x-t*w))+gamma*U(xi)^(2*n)*U(xi)*exp(I*(k*x-t*w))+delta*U(xi)^(3*n)*U(xi)*exp(I*(k*x-t*w))+lambda*U(xi)^(4*n)*U(xi)*exp(I*(k*x-t*w)) = 0

(4)

case1 := [beta = 2*RootOf(3*_Z^2-3*_Z-1)*(n+2)/(B[1]*n^2), delta = 2*B[1]*(RootOf(3*_Z^2-3*_Z-1)+1)*(3*n+2)/(3*n^2), eta = (k^2*n^2*B[1]^2-n^2*w*B[1]^2-1)/(n^2*B[1]^2), gamma = -6*RootOf(3*_Z^2-3*_Z-1)*(n+1)/n^2, lambda = B[1]^2*(3*RootOf(3*_Z^2-3*_Z-1)-7)*(2*n+1)/(9*n^2), A[0] = RootOf(3*_Z^2-3*_Z-1)*B[1], A[1] = 0, B[1] = B[1]]

[beta = 2*RootOf(3*_Z^2-3*_Z-1)*(n+2)/(B[1]*n^2), delta = (2/3)*B[1]*(RootOf(3*_Z^2-3*_Z-1)+1)*(3*n+2)/n^2, eta = (k^2*n^2*B[1]^2-n^2*w*B[1]^2-1)/(n^2*B[1]^2), gamma = -6*RootOf(3*_Z^2-3*_Z-1)*(n+1)/n^2, lambda = (1/9)*B[1]^2*(3*RootOf(3*_Z^2-3*_Z-1)-7)*(2*n+1)/n^2, A[0] = RootOf(3*_Z^2-3*_Z-1)*B[1], A[1] = 0, B[1] = B[1]]

(5)

n := 1

1

(6)

G := U(xi) = (B[1]*(RootOf(3*_Z^2-3*_Z-1)+coth(xi)))^(-1/n)

U(xi) = 1/(B[1]*(RootOf(3*_Z^2-3*_Z-1)+coth(xi)))

(7)

pde3 := eval(ode, case1)

I*(-2*(diff(U(xi), xi))*k*exp(I*(k*x-t*w))-I*U(xi)*w*exp(I*(k*x-t*w)))+(diff(diff(U(xi), xi), xi))*exp(I*(k*x-t*w))+(2*I)*(diff(U(xi), xi))*k*exp(I*(k*x-t*w))-U(xi)*k^2*exp(I*(k*x-t*w))+(k^2*B[1]^2-w*B[1]^2-1)*U(xi)*exp(I*(k*x-t*w))/B[1]^2+6*RootOf(3*_Z^2-3*_Z-1)*U(xi)^2*exp(I*(k*x-t*w))/B[1]-12*RootOf(3*_Z^2-3*_Z-1)*U(xi)^3*exp(I*(k*x-t*w))+(10/3)*B[1]*(RootOf(3*_Z^2-3*_Z-1)+1)*U(xi)^4*exp(I*(k*x-t*w))+(1/3)*B[1]^2*(3*RootOf(3*_Z^2-3*_Z-1)-7)*U(xi)^5*exp(I*(k*x-t*w)) = 0

(8)

odetest(eval(G, case1), pde3)

79584*exp(I*k*x-I*t*w+12*xi)/(B[1]*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))-127440*exp(I*k*x-I*t*w+10*xi)/(B[1]*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))+8352*exp(I*k*x-I*t*w+6*xi)/(B[1]^3*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))-27792*exp(I*k*x-I*t*w+8*xi)/(B[1]^3*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))-24*exp(2*xi-I*t*w+I*k*x)/(B[1]*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))+4752*exp(I*k*x-I*t*w+4*xi)/(B[1]^3*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))+288*exp(2*xi-I*t*w+I*k*x)/(B[1]^3*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))-479376*exp(I*k*x-I*t*w+12*xi)/(B[1]^3*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))+138240*exp(I*k*x-I*t*w+10*xi)/(B[1]^3*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))+70560*exp(18*xi+I*k*x-I*t*w)/(B[1]^3*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))-492912*exp(I*k*x-I*t*w+16*xi)/(B[1]^3*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))+777888*exp(I*k*x-I*t*w+14*xi)/(B[1]^3*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))+16608*exp(I*k*x-I*t*w+8*xi)/(B[1]*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))-1056*exp(I*k*x-I*t*w+6*xi)/(B[1]*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))+288*exp(I*k*x-I*t*w+4*xi)/(B[1]*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))-39000*exp(18*xi+I*k*x-I*t*w)/(B[1]*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))-50400*exp(I*k*x-I*t*w+16*xi)/(B[1]*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))+121440*exp(I*k*x-I*t*w+14*xi)/(B[1]*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))+27000*RootOf(3*_Z^2-3*_Z-1)*exp(18*xi+I*k*x-I*t*w)/(B[1]*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))-55080*RootOf(3*_Z^2-3*_Z-1)*exp(18*xi+I*k*x-I*t*w)/(B[1]^3*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))+7200*RootOf(3*_Z^2-3*_Z-1)*exp(I*k*x-I*t*w+16*xi)/(B[1]*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))+394416*RootOf(3*_Z^2-3*_Z-1)*exp(I*k*x-I*t*w+16*xi)/(B[1]^3*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))-205920*RootOf(3*_Z^2-3*_Z-1)*exp(I*k*x-I*t*w+14*xi)/(B[1]*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))-609984*RootOf(3*_Z^2-3*_Z-1)*exp(I*k*x-I*t*w+14*xi)/(B[1]^3*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))-244512*RootOf(3*_Z^2-3*_Z-1)*exp(I*k*x-I*t*w+12*xi)/(B[1]*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))+366768*RootOf(3*_Z^2-3*_Z-1)*exp(I*k*x-I*t*w+12*xi)/(B[1]^3*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))-42480*RootOf(3*_Z^2-3*_Z-1)*exp(I*k*x-I*t*w+10*xi)/(B[1]*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))-144720*RootOf(3*_Z^2-3*_Z-1)*exp(I*k*x-I*t*w+10*xi)/(B[1]^3*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))-48672*RootOf(3*_Z^2-3*_Z-1)*exp(I*k*x-I*t*w+8*xi)/(B[1]*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))+8208*RootOf(3*_Z^2-3*_Z-1)*exp(I*k*x-I*t*w+8*xi)/(B[1]^3*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))+9504*RootOf(3*_Z^2-3*_Z-1)*exp(I*k*x-I*t*w+6*xi)/(B[1]*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))+20736*RootOf(3*_Z^2-3*_Z-1)*exp(I*k*x-I*t*w+6*xi)/(B[1]^3*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))+288*RootOf(3*_Z^2-3*_Z-1)*exp(I*k*x-I*t*w+4*xi)/(B[1]*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))+18576*RootOf(3*_Z^2-3*_Z-1)*exp(I*k*x-I*t*w+4*xi)/(B[1]^3*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))-72*RootOf(3*_Z^2-3*_Z-1)*exp(2*xi-I*t*w+I*k*x)/(B[1]*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))+1080*RootOf(3*_Z^2-3*_Z-1)*exp(2*xi-I*t*w+I*k*x)/(B[1]^3*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))

(9)

simplify(-492912*exp(I*k*x-I*t*w+16*xi)/(B[1]^3*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))+777888*exp(I*k*x-I*t*w+14*xi)/(B[1]^3*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))+16608*exp(I*k*x-I*t*w+8*xi)/(B[1]*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))-1056*exp(I*k*x-I*t*w+6*xi)/(B[1]*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))+288*exp(I*k*x-I*t*w+4*xi)/(B[1]*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))-39000*exp(18*xi+I*k*x-I*t*w)/(B[1]*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))-50400*exp(I*k*x-I*t*w+16*xi)/(B[1]*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))+121440*exp(I*k*x-I*t*w+14*xi)/(B[1]*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))+79584*exp(I*k*x-I*t*w+12*xi)/(B[1]*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))-127440*exp(I*k*x-I*t*w+10*xi)/(B[1]*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))+8352*exp(I*k*x-I*t*w+6*xi)/(B[1]^3*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))-27792*exp(I*k*x-I*t*w+8*xi)/(B[1]^3*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))-24*exp(2*xi-I*t*w+I*k*x)/(B[1]*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))+4752*exp(I*k*x-I*t*w+4*xi)/(B[1]^3*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))+288*exp(2*xi-I*t*w+I*k*x)/(B[1]^3*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))-479376*exp(I*k*x-I*t*w+12*xi)/(B[1]^3*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))+138240*exp(I*k*x-I*t*w+10*xi)/(B[1]^3*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))+70560*exp(18*xi+I*k*x-I*t*w)/(B[1]^3*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))-55080*RootOf(3*_Z^2-3*_Z-1)*exp(18*xi+I*k*x-I*t*w)/(B[1]^3*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))+7200*RootOf(3*_Z^2-3*_Z-1)*exp(I*k*x-I*t*w+16*xi)/(B[1]*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))+394416*RootOf(3*_Z^2-3*_Z-1)*exp(I*k*x-I*t*w+16*xi)/(B[1]^3*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))-205920*RootOf(3*_Z^2-3*_Z-1)*exp(I*k*x-I*t*w+14*xi)/(B[1]*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))-609984*RootOf(3*_Z^2-3*_Z-1)*exp(I*k*x-I*t*w+14*xi)/(B[1]^3*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))-244512*RootOf(3*_Z^2-3*_Z-1)*exp(I*k*x-I*t*w+12*xi)/(B[1]*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))+366768*RootOf(3*_Z^2-3*_Z-1)*exp(I*k*x-I*t*w+12*xi)/(B[1]^3*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))-42480*RootOf(3*_Z^2-3*_Z-1)*exp(I*k*x-I*t*w+10*xi)/(B[1]*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))-144720*RootOf(3*_Z^2-3*_Z-1)*exp(I*k*x-I*t*w+10*xi)/(B[1]^3*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))-48672*RootOf(3*_Z^2-3*_Z-1)*exp(I*k*x-I*t*w+8*xi)/(B[1]*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))+8208*RootOf(3*_Z^2-3*_Z-1)*exp(I*k*x-I*t*w+8*xi)/(B[1]^3*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))+9504*RootOf(3*_Z^2-3*_Z-1)*exp(I*k*x-I*t*w+6*xi)/(B[1]*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))+20736*RootOf(3*_Z^2-3*_Z-1)*exp(I*k*x-I*t*w+6*xi)/(B[1]^3*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))+288*RootOf(3*_Z^2-3*_Z-1)*exp(I*k*x-I*t*w+4*xi)/(B[1]*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))+18576*RootOf(3*_Z^2-3*_Z-1)*exp(I*k*x-I*t*w+4*xi)/(B[1]^3*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))-72*RootOf(3*_Z^2-3*_Z-1)*exp(2*xi-I*t*w+I*k*x)/(B[1]*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))+1080*RootOf(3*_Z^2-3*_Z-1)*exp(2*xi-I*t*w+I*k*x)/(B[1]^3*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))+27000*RootOf(3*_Z^2-3*_Z-1)*exp(18*xi+I*k*x-I*t*w)/(B[1]*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1)))

(((244512*B[1]^2-366768)*exp(10*xi)+(205920*B[1]^2+609984)*exp(12*xi)+(-7200*B[1]^2-394416)*exp(14*xi)+42480*exp(8*xi)*B[1]^2-27000*exp(16*xi)*B[1]^2-288*exp(2*xi)*B[1]^2-9504*exp(4*xi)*B[1]^2+48672*exp(6*xi)*B[1]^2+72*B[1]^2+144720*exp(8*xi)+55080*exp(16*xi)-18576*exp(2*xi)-20736*exp(4*xi)-8208*exp(6*xi)-1080)*RootOf(3*_Z^2-3*_Z-1)+(-79584*B[1]^2+479376)*exp(10*xi)+(-121440*B[1]^2-777888)*exp(12*xi)+(50400*B[1]^2+492912)*exp(14*xi)+127440*exp(8*xi)*B[1]^2+39000*exp(16*xi)*B[1]^2-288*exp(2*xi)*B[1]^2+1056*exp(4*xi)*B[1]^2-16608*exp(6*xi)*B[1]^2+24*B[1]^2-138240*exp(8*xi)-70560*exp(16*xi)-4752*exp(2*xi)-8352*exp(4*xi)+27792*exp(6*xi)-288)*exp(2*xi-I*t*w+I*k*x)/(B[1]^3*(-3125*exp(20*xi)-25000*exp(18*xi)-76875*exp(16*xi)-108000*exp(14*xi)-55650*exp(12*xi)+12432*exp(10*xi)+11130*exp(8*xi)-4320*exp(6*xi)+615*exp(4*xi)-40*exp(2*xi)+1))

(10)

Download ode.mw

this is my first time something like that   coming up my equation after taking integral exponential coming up why?

g1.mw

the series is so complicated but have a strange pattern if you watch the index of parameter  they are not repeated 

 

 

How i can get FN from N-soliton to FN for M-lump by applying long wave method and using limit How we can get the series of lump , there is some example for nowing how lump work like f[2] for 1 lump and f[4] for two lump and f[6] for 3 lump i, and also in last of work i showed the series of for n soliton which we can change it to m-lump  but i don't know how work and a[12] will change to b[12] by applying long wave method

m-lump.mw

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