7 papers
Numerical analysis of a self-similar turbulent flow in Bose--Einstein condensates
B. V. Semisalov, V. N. Grebenev, S. B. Medvedev +1
We study a self-similar solution of the kinetic equation describing weak wave turbulence in Bose-Einstein condensates. This solution presumably corresponds to an asymptotic behavio…
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)…
Steady states in dual-cascade wave turbulence
V. N. Grebenev, S. B. Medvedev, S. V. Nazarenko +1
We study stationary solutions in the differential kinetic equation, which was introduced in for description of a local dual cascade wave turbulence. We give a full classification o…
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…