We study asymptotic behaviour at time infinity of solutions close to the non-zero constant
equilibrium for the Gross–Pitaevskii equation in two and three spatial dimensions. We construct …

Nonlinear Schrödinger equations (NLSs) with focusing power nonlinearities have solitary
wave solutions. The spectra of the linearized operators around these solitary waves are …

We consider the Landau-Lifshitz equations of ferromagnetism (including the harmonic map
heat-flow and Schrödinger flow as special cases) for degree m equivariant maps from $${\…

Acknowledgment: The authors are grateful to R. Frank, M. Lemm, B. Nachtergaele and S.
Teufel for reading parts of the new material and making many pertinent remarks.

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 H 1 , and …

We study the motion of solitary-wave solutions of a family of focusing generalized nonlinear
Schroedinger equations with a confining, slowly varying external potential, $V(x)$. A …

We investigate the asymptotic behavior at time infinity of solutions close to a non-zero constant
equilibrium for the Gross-Pitaevskii (or Ginzburg-Landau Schroedinger) equation. We …

We present new interior regularity criteria for suitable weak solutions of the 3-D Navier-Stokes
equations: a suitable weak solution is regular near an interior point z if either the scaled $$…

We study the global behavior of small solutions of the Gross–Pitaevskii equation in three
dimensions. We prove that disturbances from the constant equilibrium with small, localized …

For Schrödinger maps from R 2 × R + to the 2 -sphere S 2 , it is not known if finite energy
solutions can form singularities (blow up) in finite time. We consider equivariant solutions with …