31 citations · 96 across the 12 of their papers we have counts for
13 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…
High-Order Block Toeplitz Inner-Bordering method for solving the Gelfand-Levitan-Marchenko equation
Sergey Medvedev, Irina Vaseva, Mikhail Fedoruk
We propose a high precision algorithm for solving the Gelfand-Levitan-Marchenko equation. The algorithm is based on the block version of the Toeplitz Inner-Bordering algorithm of L…
Processing of optical signals by "surgical" methods for the Gelfand-Levitan-Marchenko equation
Sergey Medvedev, Irina Vaseva, Mikhail Fedoruk
We propose a new method for solving the Gelfand-Levitan-Marchenko equation (GLME) based on the block version of the Toeplitz Inner-Bordering (TIB) with an arbitrary point to start…
Inverse cascade anomalies in fourth-order Leith models
Simon Thalabard, Sergey Medvedev, Vladimir Grebenev +1
We analyze a family of fourth-order non-linear diffusion models corresponding to local approximations of 4-wave kinetic equations of weak wave turbulence. We focus on a class of pa…
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…
Novel Numerical Algorithm with Fourth-Order Accuracy for the Direct Zakharov-Shabat Problem
Sergey Medvedev, Irina Vaseva, Igor Chekhovskoy +1
We propose a new high-precision algorithm for solving the initial problem for the Zakharov-Shabat system. This method has the fourth order of accuracy and is a generalization of th…
Anomalous spectral laws in differential models of turbulence
Simon Thalabard, Sergey Nazarenko, Sebastien Galtier +1
Differential models for hydrodynamic, passive-scalar and wave turbulence given by nonlinear first- and second-order evolution equations for the energy spectrum in the -space wer…
Wave turbulence in the two-layer ocean model
Katie L Harper, Sergey V Nazarenko, Sergey B Medvedev +1
This paper looks at the two-layer ocean model from a wave turbulence perspective. A symmetric form of the two-layer kinetic equation for Rossby waves is derived using canonical var…