7 citations · 11 across the 5 of their papers we have counts for
5 papers
Existence and stability of standing waves for one dimensional NLS with triple power nonlinearities
Fei Liu, Tai-Peng Tsai, Ian Zwiers
In this note we study analytically and numerically the existence and stability of standing waves for one dimensional nonlinear Schrödinger equations whose nonlinearities are the su…
Adaptive finite difference methods for nonlinear elliptic and parabolic partial differential equations with free boundaries
Adam M. Oberman, Ian Zwiers
Monotone finite difference methods provide stable convergent discretizations of a class of degenerate elliptic and parabolic Partial Differential Equations (PDEs). These methods ar…
Local Dynamics Near Unstable Branches of NLS Solitons
Vianney Combet, Tai-Peng Tsai, Ian Zwiers
Consider a branch of unstable solitons of NLS whose linearized operators have one pair of simple real eigenvalues in addition to the zero eigenvalue. Under radial symmetry and stan…
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…
Standing Ring Blowup Solutions for Cubic NLS
Ian Zwiers
We prove there exist solutions to the focusing cubic nonlinear Schrödinger equation in three dimensions that blowup on a circle, in the sense of L^2 concentration on a ring, bounde…