12 citations · 49 across the 11 of their papers we have counts for
11 papers
Whitham modulation theory for the Davey-Stewartson system and stability analysis of its periodic traveling wave solutions
Gino Biondini, Alexander Chernyavsky, Haodong Lin +1
The Davey-Stewartson (DS) system is a canonical model for a weakly nonlinear wave packet in two spatial dimensions that is resonantly coupled to the slowly varying mean flow it gen…
Whitham modulation theory for the Zakharov-Kuznetsov equation and transverse instability of its periodic traveling wave solutions
Gino Biondini, Alexander Chernyavsky
We derive the Whitham modulation equations for the Zakharov-Kuznetsov equation via a multiple scales expansion and averaging two conservation laws over one oscillation period of it…
Integrability and trajectory confinement in -symmetric waveguide arrays
I V Barashenkov, Frank Smuts, Alexander Chernyavsky
We consider -symmetric ring-like arrays of optical waveguides with purely nonlinear gain and loss. Regardless of the value of the gain-loss coefficient, these systems…
Right and left inverse scattering problems formulations for the Zakharov-Shabat system
Alexander Chernyavsky, Leonid Frumin, Andrey Gelash
We consider right and left formulations of the inverse scattering problem for the Zakharov-Shabat system and the corresponding integral Gelfand-Levitan-Marchenko equations. Both fo…
Dynamics of D fluid in bounded domain via conformal variables
Alexander Chernyavsky, Sergey Dyachenko
In the present work we compute numerical solutions of an integro-differential equation for traveling waves on the boundary of a D blob of an ideal fluid in the presence of surfa…
Convex relaxations of integral variational problems: pointwise dual relaxation and sum-of-squares optimization
Alexander Chernyavsky, Jason J. Bramburger, Giovanni Fantuzzi +1
We present a method for finding lower bounds on the global infima of integral variational problems, wherein is minimized over functions $u\col…
Stable solitons in a nearly PT-symmetric ferromagnet with spin-transfer torque
I. V. Barashenkov, Alexander Chernyavsky
We consider the Landau-Lifshitz equation for the spin torque oscillator - a uniaxial ferromagnet in an external magnetic field with polarised spin current driven through it. In the…
Krein Signature in Hamiltonian and -symmetric Systems
A. Chernyavsky, P. G. Kevrekidis, D. E. Pelinovsky
We explain the concept of Krein signature in Hamiltonian and -symmetric systems on the case study of the one-dimensional Gross-Pitaevskii equation with a real harmoni…
Krein signature for instability of -symmetric states
Alexander Chernyavsky, Dmitry E. Pelinovsky
Krein quantity is introduced for isolated neutrally stable eigenvalues associated with the stationary states in the -symmetric nonlinear Schrödinger equation. Krein q…
Long-time stability of breathers in Hamiltonian -symmetric lattices
Alexander Chernyavsky, Dmitry E. Pelinovsky
We consider the Hamiltonian version of a -symmetric lattice that describes dynamics of coupled pendula under a resonant periodic force. Using the asymptotic limit of a wea…
Breathers in Hamiltonian -symmetric chains of coupled pendula under a resonant periodic force
Alexander Chernyavsky, Dmitry E. Pelinovsky
We derive a Hamiltonian version of the -symmetric discrete nonlinear Schrödinger equation that describes synchronized dynamics of coupled pendula driven by a periodic mo…