- #1
Johnbasko
- 5
- 0
Hello all,
I have short question at the end , but i wil gve short background.
The subject is regarding the split step Fourier method (SSFM) adn i will be gratefull if someone who know the method can help.
i have the set of 2 equations:
Utt=Uzz-a*U+i*P-(P^2)*U
Pt=-i*P-(P^2)*U
where: P, U are the function need to be find P(z,t) U(z,t)
i = sqrt(-1) a=constant
I try to do the split step Fourier method (SSFM) on this set, the problem is that the first equation derivative are from order 2, and in all the examples i saw it was from order 1.
I try to separate to linear part and nonlinear part:
for the first equation:
U_linear_tt=Uzz-a*U
U_nonlinear_tt= i*P-(P^2)*U
and for the second equation:
P_linear_t=-i*P
P_nonlinear_t=-(P^2)*U
now when i try to do the Fourier transform at the linear part, for the U function, it is problem because the derivative is second order.
if it was from first order the Fourier transform for the linear part becomes:
Fourier_U_linear(t+dt,z)=exp{(-w^2-a)*dt}
how do i modified it on my case when the derivative is second order ?
thanks
I have short question at the end , but i wil gve short background.
The subject is regarding the split step Fourier method (SSFM) adn i will be gratefull if someone who know the method can help.
i have the set of 2 equations:
Utt=Uzz-a*U+i*P-(P^2)*U
Pt=-i*P-(P^2)*U
where: P, U are the function need to be find P(z,t) U(z,t)
i = sqrt(-1) a=constant
I try to do the split step Fourier method (SSFM) on this set, the problem is that the first equation derivative are from order 2, and in all the examples i saw it was from order 1.
I try to separate to linear part and nonlinear part:
for the first equation:
U_linear_tt=Uzz-a*U
U_nonlinear_tt= i*P-(P^2)*U
and for the second equation:
P_linear_t=-i*P
P_nonlinear_t=-(P^2)*U
now when i try to do the Fourier transform at the linear part, for the U function, it is problem because the derivative is second order.
if it was from first order the Fourier transform for the linear part becomes:
Fourier_U_linear(t+dt,z)=exp{(-w^2-a)*dt}
how do i modified it on my case when the derivative is second order ?
thanks