191 citations · 878 across the 41 of their papers we have counts for
42 papers
Lower bound for the rate of blow-up of singular solutions of the Zakharov system in
J. Colliander, M. Czubak, C. Sulem
We consider the scalar Zakharov system in for initial conditions , . Assuming that…
Behavior of a Model Dynamical System with Applications to Weak Turbulence
James E. Colliander, Jeremy L. Marzuola, Tadahiro Oh +1
We experimentally explore solutions to a model Hamiltonian dynamical system derived in Colliander et al., 2012, to study frequency cascades in the cubic defocusing nonlinear Schröd…
Interaction Morawetz estimate for the magnetic Schrödinger equation and applications
James Colliander, Magdalena Czubak, Jeonghun Lee
We establish an interaction Morawetz estimate for the magnetic Schrödinger equation for under certain smallness conditions on the gauge potentials, but with almost optima…
A remark on normal forms and the "upside-down" I-method for periodic NLS: growth of higher Sobolev norms
James Colliander, Soonsik Kwon, Tadahiro Oh
We study growth of higher Sobolev norms of solutions to the one-dimensional periodic nonlinear Schrodinger equation (NLS). By a combination of the normal form reduction and the ups…
Numerical simulations of the energy- supercritical Nonlinear Schrödinger equation
J. Colliander, G. Simpson, C. Sulem
We present numerical simulations of the defocusing nonlinear Schrodinger (NLS) equation with an energy supercritical nonlinearity. These computations were motivated by recent works…
Remarks on global a priori estimates for the nonlinear Schrödinger equation
J. Colliander, M. Grillakis, N. Tzirakis
We present a unified approach for obtaining global a priori estimates for solutions of nonlinear defocusing Schrödinger equations with defocusing nonlinearities. The estimates are…