| Abstract: | Soliton solutions are constructed numerically for the problem of propagation of a femtosecond pulse in a medium with a cubic
nonlinearity. The problem is posed as an eigenvalue problem with an operator nonlinear in the eigenfunctions. For given values
of the propagation parameter we find the real eigenvalue λ and the corresponding eigenvector. This eigenvector is a soliton,
i.e., a solution that does not vary in the coordinate of propagation of the light pulse. An algorithm is proposed to find
the minimum eigenvalue and the corresponding eigenfunctions that satisfy given conditions.
Translated from Prikladnaya Matematika i Informatika, No. 2, pp. 63–68, 1999. |
