Help in Split step fourier method

  1. 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 seperate 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
     
  2. jcsd
  3. I try to do the split step fourier method (SSFM)
     
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