This is a survey of the theory of attractors of nonlinear Hamiltonian partial differential
equations since its appearance in 1990. Included are results on global attraction to …

It is shown that for a one-dimensional Schrödinger operator with a potential whose first
moment is integrable the elements of the scattering matrix are in the unital Wiener algebra of …

We consider quantum walks with position dependent coin on 1D lattice Z. The dispersive
estimate∥ UtPcu0∥ l∞≲(1+| t|)− 1/3∥ u0∥ l1 is shown under l1, 1 perturbation for the …

In this paper, we study the long time behavior of nonlinear quantum walks when the initial
data is small in l 2. In particular, we study the case where the linear part of the quantum walk …

We address the problem of long-time asymptotics for the solutions of the Korteweg–de Vries
equation under low regularity assumptions. We consider decaying initial data admitting only …

We derive a dispersion estimate for one-dimensional perturbed radial Schrödinger
operators. We also derive several new estimates for solutions of the underlying differential …

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The primary objective of this paper is to investigate the well-posedness theories associated
with the discrete nonlinear Schr\" odinger equation and Klein-Gordon equation. These …

We consider the one-dimensional discrete Schrödinger operator on ℤ, and study the relation
between the generalized eigenstates and the asymptotic expansion of the resolvent for the …

We apply weighted Mourre commutator theory to prove the limiting absorption principle for
the discrete Schrödinger operator perturbed by the sum of a Wigner–von Neumann and long …