Semi-classical Schrödinger equations with harmonic potential and nonlinear perturbation
Rémi Carles (2003)
Annales de l'I.H.P. Analyse non linéaire
David Borthwick, Thierry Paul, Alejandro Uribe (1998)
Annales de l'institut Fourier
Let be a compact Kähler manifold with integral Kähler class and a holomorphic Hermitian line bundle whose curvature is the symplectic form of . Let be a Hamiltonian, and let be the Toeplitz operator with multiplier acting on the space . We obtain estimates on the eigenvalues and eigensections of as , in terms of the classical Hamilton flow of . We study in some detail the case when is an integral coadjoint orbit of a Lie group.
Eugenio Montefusco, Benedetta Pellacci, Marco Squassina (2008)
Journal of the European Mathematical Society
We consider systems of weakly coupled Schrödinger equations with nonconstant potentials and investigate the existence of nontrivial nonnegative solutions which concentrate around local minima of the potentials. We obtain sufficient and necessary conditions for a sequence of least energy solutions to concentrate.
Antonio Ambrosetti, Marino Badiale, Silvia Cingolani (1996)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
Using some perturbation results in critical point theory, we prove that a class of nonlinear Schrödinger equations possesses semiclassical states that concentrate near the critical points of the potential .
Giuseppe Buttazzo, Berardo Ruffini, Bozhidar Velichkov (2014)
ESAIM: Control, Optimisation and Calculus of Variations
Γ):Γ ∈ 𝒜, ℋ1(Γ) = l}, where ℋ1D1,...,Dk } ⊂ Rd . The cost functional ℰ(Γ) is the Dirichlet energy of Γ defined through the Sobolev functions on Γ vanishing on the points Di. We analyze the existence of a solution in both the families of connected sets and of metric graphs. At the end, several explicit examples are discussed.
Rosu, Haret C., Khmelnytskaya, Kira V. (2011)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
Calaque, Damien, Rossi, Carlo A. (2008)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
Luc Miller (1997)
Journées équations aux dérivées partielles
M. Göteman, Ulf Lindström (2010)
Archivum Mathematicum
We discuss additional supersymmetries for supersymmetric non-linear sigma models described by left and right semichiral superfields.
Luigi Accardi, Yukihiro Hashimoto, Nobuaki Obata (1998)
Banach Center Publications
Motivated by the central limit problem for algebraic probability spaces arising from the Haagerup states on the free group with countably infinite generators, we introduce a new notion of statistical independence in terms of inequalities rather than of usual algebraic identities. In the case of the Haagerup states the role of the Gaussian law is played by the Ullman distribution. The limit process is realized explicitly on the finite temperature Boltzmannian Fock space. Furthermore, a functional...
Yves Colin de Verdière, San Vũ Ngọc (2003)
Annales scientifiques de l'École Normale Supérieure
Langmann, Edwin (2007)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
Schneider, Baruch (2005)
Electronic Journal of Differential Equations (EJDE) [electronic only]
Fülöp, Tamás (2007)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
Vladimir G. Turaev (1991)
Annales scientifiques de l'École Normale Supérieure
Shuji Machihara, Kenji Nakanishi, Tohru Ozawa (2003)
Revista Matemática Iberoamericana
In this paper we study the Cauchy problem for the nonlinear Dirac equation in the Sobolev space Hs. We prove the existence and uniqueness of global solutions for small data in Hs with s > 1...
Simonetta Abenda (1998)
Annales de l'I.H.P. Physique théorique
Coclite, Giuseppe Maria, Georgiev, Vladimir (2004)
Electronic Journal of Differential Equations (EJDE) [electronic only]
K. Kirkpatrick (2012)
Mathematical Modelling of Natural Phenomena
We review some recent results concerning Gibbs measures for nonlinear Schrödinger equations (NLS), with implications for the theory of the NLS, including stability and typicality of solitary wave structures. In particular, we discuss the Gibbs measures of the discrete NLS in three dimensions, where there is a striking phase transition to soliton-like behavior.
Alain Bachelot (1987)
Journées équations aux dérivées partielles