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Neural fields with sigmoidal firing rates: Approximate solutions
A general description of quantum dynamical spreading over an orthonormal basis and applications to Schrödinger operators
1. | Department of Mathematics, Rice University, Houston, TX 77005 |
2. | UMR 6628–MAPMO, Université d’Orléans, B.P. 6759, F-45067 Orléans Cedex, France |
[1] |
Jaime Cruz-Sampedro. Schrödinger-like operators and the eikonal equation. Communications on Pure and Applied Analysis, 2014, 13 (2) : 495-510. doi: 10.3934/cpaa.2014.13.495 |
[2] |
José Luis López. A quantum approach to Keller-Segel dynamics via a dissipative nonlinear Schrödinger equation. Discrete and Continuous Dynamical Systems, 2021, 41 (6) : 2601-2617. doi: 10.3934/dcds.2020376 |
[3] |
Harald Friedrich. Semiclassical and large quantum number limits of the Schrödinger equation. Conference Publications, 2003, 2003 (Special) : 288-294. doi: 10.3934/proc.2003.2003.288 |
[4] |
Takahisa Inui. Global dynamics of solutions with group invariance for the nonlinear schrödinger equation. Communications on Pure and Applied Analysis, 2017, 16 (2) : 557-590. doi: 10.3934/cpaa.2017028 |
[5] |
Hiroshi Isozaki, Hisashi Morioka. A Rellich type theorem for discrete Schrödinger operators. Inverse Problems and Imaging, 2014, 8 (2) : 475-489. doi: 10.3934/ipi.2014.8.475 |
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Fritz Gesztesy, Roger Nichols. On absence of threshold resonances for Schrödinger and Dirac operators. Discrete and Continuous Dynamical Systems - S, 2020, 13 (12) : 3427-3460. doi: 10.3934/dcdss.2020243 |
[7] |
Fengping Yao. Optimal regularity for parabolic Schrödinger operators. Communications on Pure and Applied Analysis, 2013, 12 (3) : 1407-1414. doi: 10.3934/cpaa.2013.12.1407 |
[8] |
Jean Bourgain. On quasi-periodic lattice Schrödinger operators. Discrete and Continuous Dynamical Systems, 2004, 10 (1&2) : 75-88. doi: 10.3934/dcds.2004.10.75 |
[9] |
Jean Bourgain. On random Schrödinger operators on $\mathbb Z^2$. Discrete and Continuous Dynamical Systems, 2002, 8 (1) : 1-15. doi: 10.3934/dcds.2002.8.1 |
[10] |
Camille Laurent. Internal control of the Schrödinger equation. Mathematical Control and Related Fields, 2014, 4 (2) : 161-186. doi: 10.3934/mcrf.2014.4.161 |
[11] |
Claude Bardos, François Golse, Peter Markowich, Thierry Paul. On the classical limit of the Schrödinger equation. Discrete and Continuous Dynamical Systems, 2015, 35 (12) : 5689-5709. doi: 10.3934/dcds.2015.35.5689 |
[12] |
D.G. deFigueiredo, Yanheng Ding. Solutions of a nonlinear Schrödinger equation. Discrete and Continuous Dynamical Systems, 2002, 8 (3) : 563-584. doi: 10.3934/dcds.2002.8.563 |
[13] |
Frank Wusterhausen. Schrödinger equation with noise on the boundary. Conference Publications, 2013, 2013 (special) : 791-796. doi: 10.3934/proc.2013.2013.791 |
[14] |
Shi Jin, Peng Qi. A hybrid Schrödinger/Gaussian beam solver for quantum barriers and surface hopping. Kinetic and Related Models, 2011, 4 (4) : 1097-1120. doi: 10.3934/krm.2011.4.1097 |
[15] |
Roberto de A. Capistrano–Filho, Márcio Cavalcante, Fernando A. Gallego. Forcing operators on star graphs applied for the cubic fourth order Schrödinger equation. Discrete and Continuous Dynamical Systems - B, 2022, 27 (6) : 3399-3434. doi: 10.3934/dcdsb.2021190 |
[16] |
Diana Keller. Optimal control of a linear stochastic Schrödinger equation. Conference Publications, 2013, 2013 (special) : 437-446. doi: 10.3934/proc.2013.2013.437 |
[17] |
Pavel I. Naumkin, Isahi Sánchez-Suárez. On the critical nongauge invariant nonlinear Schrödinger equation. Discrete and Continuous Dynamical Systems, 2011, 30 (3) : 807-834. doi: 10.3934/dcds.2011.30.807 |
[18] |
Alexander Arbieto, Carlos Matheus. On the periodic Schrödinger-Debye equation. Communications on Pure and Applied Analysis, 2008, 7 (3) : 699-713. doi: 10.3934/cpaa.2008.7.699 |
[19] |
Rossella Bartolo, Anna Maria Candela, Addolorata Salvatore. Infinitely many solutions for a perturbed Schrödinger equation. Conference Publications, 2015, 2015 (special) : 94-102. doi: 10.3934/proc.2015.0094 |
[20] |
Tarek Saanouni. Remarks on the damped nonlinear Schrödinger equation. Evolution Equations and Control Theory, 2020, 9 (3) : 721-732. doi: 10.3934/eect.2020030 |
2020 Impact Factor: 1.392
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