5 papers
Fast eight-order Pade schemes based on Chebyshev polynomials for direct Zakharov-Shabat problem
Sergey Medvedev, Igor Chekhovskoy, Irina Vaseva +1
In this work, we construct fast eighth-order Pade schemes for the direct Zakharov-Shabat scattering problem. The schemes are based on an eighth-order exponential integrator obtaine…
Fast sixth-order algorithm based on the generalized Cayley transform for the Zakharov-Shabat system in optical applications
Sergey Medvedev, Igor Chekhovskoy, Irina Vaseva +1
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 i…
Introducing phase jump tracking -- a fast method for eigenvalue evaluation of the direct Zakharov-Shabat problem
Igor Chekhovskoy, Sergey Medvedev, Irina Vaseva +2
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 $a(ζ)…
Fast Computation of the Direct Scattering Transform by Fourth Order Conservative Multi-Exponential Scheme
Sergey Medvedev, Igor Chekhovskoy, Irina Vaseva +1
A fourth-order multi-exponential scheme is proposed for the Zakharov-Shabat system. The scheme represents a product of 13 exponential operators. The construction of the scheme is b…
Exponential Fourth Order Schemes for Direct Zakharov-Shabat problem
Sergey Medvedev, Irina Vaseva, Igor Chekhovskoy +1
We propose two finite-difference algorithms of fourth order of accuracy for solving the initial problem of the Zakharov-Shabat system. Both schemes have the exponential form and co…