178 citations · 185 across the 6 of their papers we have counts for
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math.AP2003
Effective Dynamics of Magnetic Vortices
S. Gustafson, I. M. Sigal
We study solutions of Ginzburg-Landau-type evolution equations (both dissipative and Hamiltonian) with initial data representing collections of widely-spaced vortices. We show that…
math-ph2003★ 178 cited
Solitary Wave Dynamics in an External Potential
J. Frohlich, S. Gustafson, B. L. G. Jonsson +1
We study the behavior of solitary-wave solutions of some generalized nonlinear Schrödinger equations with an external potential. The equations have the feature that in the absence…
math-ph2003★ 7 cited
Asymptotic Stability and Completeness in the Energy Space for Nonlinear Schrödinger Equations with Small Solitary Waves
Stephen Gustafson, Kenji Nakanishi, Tai-Peng Tsai
In this paper we study a class of nonlinear Schrödinger equations which admit families of small solitary wave solutions. We consider solutions which are small in the energy space $…