2 research outputs found
Introducing phase jump tracking -- a fast method for eigenvalue evaluation of the direct Zakharov-Shabat problem
We propose a new method for finding discrete eigenvalues for the direct
Zakharov-Shabat problem, based on moving in the complex plane along the
argument jumps of the function , the localization of which does not
require great accuracy. It allows to find all discrete eigenvalues taking into
account their multiplicity faster than matrix methods and contour integrals.
The method shows significant advantage over other methods when calculating a
large discrete spectrum, both in speed and accuracy
Fast sixth-order algorithm based on the generalized Cayley transform for the Zakharov-Shabat system in optical applications
Based on the generalized Cayley transform, a family of conservative one-step
schemes of the sixth order of accuracy for the Zakharov-Shabat system is
constructed. The exponential integrator is a special case. Schemes based on
rational approximation allow the use of fast algorithms to solve the initial
problem for a large number of values of the spectral parameter