Displaying similar documents to “On the Ginzburg-Landau and related equations”

Dynamical instability of symmetric vortices.

Luis Almeida, Yan Guo (2001)

Revista Matemática Iberoamericana

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Using the Maxwell-Higgs model, we prove that linearly unstable symmetric vortices in the Ginzburg-Landau theory are dynamically unstable in the H1 norm (which is the natural norm for the problem). In this work we study the dynamic instability of the radial solutions of the Ginzburg-Landau equations in R2 (...)

Mean-Field Limit of Quantum Bose Gases and Nonlinear Hartree Equation

Jürg Fröhlich, Enno Lenzmann (2003-2004)

Séminaire Équations aux dérivées partielles

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We discuss the Hartree equation arising in the mean-field limit of large systems of bosons and explain its importance within the class of nonlinear Schrödinger equations. Of special interest to us is the Hartree equation with focusing nonlinearity (attractive two-body interactions). Rigorous results for the Hartree equation are presented concerning: 1) its derivation from the quantum theory of large systems of bosons, 2) existence and stability of Hartree solitons, and 3) its point-particle...