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math.AP2013★ 2 cited
Focusing Singularity in a Derivative Nonlinear Schrödinger Equation
Xiao Liu, Gideon Simpson, Catherine Sulem
We present a numerical study of a derivative nonlinear Schrödinger equation with a general power nonlinearity, . In the -supercritical regime, , our simulati…
math.AP2012
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…
math.AP2010★ 2 cited
Vortex Collapse for the L2-Critical Nonlinear Schrödinger Equation
Gideon Simpson, Ian Zwiers
The focusing cubic nonlinear Schrödinger equation in two dimensions admits vortex solitons, standing wave solutions with spatial structure, Qm(r,theta) = e^{i m theta} Rm(r). In th…