26 citations · 76 across the 17 of their papers we have counts for
20 papers
Maximal Multiplicity Method for Optimal Damping Problem
Maxim Arnold, Oleg Gendelman, Vadim Zharnitsky
We study the problem of designing optimal damping for a system of coupled linear oscillators. Using the Weyl--Horn theorem, we construct an explicit damping matrix that realize…
Critical damping in linear system with two degrees of freedom: surprises and pitfalls
Maxim D. Arnold, Oleg V. Gendelman, Vadim Zharnitsky
In this Brief Communication, we establish the notion of critical damping for generic two-degree-of-freedom system. For given set of masses and stiffnesses, the critical damping cor…
Whispering gallery orbits in Sinai oscillator trap
Ariel Lerman, Vadim Zharnitsky
Experimental realizations of trapping Bose Einstein condensate lead to a Hamiltonian system of a classical particle bouncing off a convex scatterer in the field of an attracting po…
Almost Lyapunov Functions for Nonlinear Systems
Shenyu Liu, Daniel Liberzon, Vadim Zharnitsky
We study convergence of nonlinear systems in the presence of an `almost Lyapunov' function which, unlike the classical Lyapunov function, is allowed to be nondecreasing---and even…
Critical points of Strichartz functional
C. Eugene Wayne, Vadim Zharnitsky
We study a pair of infinite dimensional dynamical systems naturally associated with the study of minimizing/maximizing functions for the Strichartz inequalities for the Schrödinger…
Solitary waves in nonlocal NLS with dispersion averaged saturated nonlinearities
Dirk Hundertmark, Young-Ran Lee, Tobias Ried +1
A nonlinear Schrödinger equation (NLS) with dispersion averaged nonlinearity of saturated type is considered. Such a nonlocal NLS is of integro-differential type and it arises natu…