Papers

Linear dispersive theory

  1. J.L. Journé, A. Soffer and C.S. Sogge, NEEDS CHANGE Estimates for time dependent Schrödinger Equations, Bull., AMS, 23, No. 2, 1990.
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Quantum resonances

  1. A. Soffer, M. Weinstein, Time Dependent resonance theory, Geometric and Functional Analysis, (GAFA) 8, 1998, 1086-1128.
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  2. A. Soffer, M. Weinstein, Nonautonomous Hamiltonians, J. Stat. Phys., 93, 1998, 359-391.
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  3. A. Soffer, M. Weinstein, Ionization and scattering for short lived potentials, Lett. Math. Phys., 1999, 48, No.4, 339-352.
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  4. P. Miller, A. Soffer, M. Weinstein, Methastability of Breather modes of Time Dependent Potentials, Nonlinearity, 13, (2000), 507-568.
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  5. O. Costin, A. Soffer, Resonance theory for Schrödinger Operators, Comm. Math. Phys., 224, (2001), 133-152.
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Rigorous numerical schemes

  1. A. Soffer, C. Stucchio, Reflectionless Propagation Algorithm for the Schrödinger Equation, (2006),   100+ pages.
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  2. A. Soffer, C. Stucchio, Open Boundaries for the Nonlinear Schrödinger Equation, J. Comp. Physics, 225, No.2 (2007) 1218-1262.
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  3. A. Soffer, C. Stucchio, Multiscale Resolution of Shortwave-Longwave Interaction, Comm. Pure Appl. Math Vol. LXII 0082-0124 (2009)
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  4. A. Soffer, C. Stucchio, Stable Open boundaries for Anisotropic waves, preprint (2008).
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Scattering on manifolds

  1. P. Blue, A. Soffer, Semilinear wave equations on the Schwarzschild manifold I:local decay, Advances in Dif. Eqs., 8, No. 5 (2003), 595-614.
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  2. P. Blue, A. Soffer, Phase space analysis on some black hole manifolds J. Func. Analysis,256 (2009) No. 1, 1-90.
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  3. W. Schlag, A. Soffer, W. Staubach, Decay estimates for the Schrödinger Evolution on asymptotically conic surfaces of revolution I, Trans. Amer. Math Soc. 362 (2010) No.1, 289-318
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  4. P. Blue, A. Soffer, Improved decay rates with small regularity loss for the wave equation about a Schwarzschild black hole, Preprint (40 pages) (2007), submitted.
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  5. P. Blue, A. Soffer, A space-time integral estimate for large data semi-linear wave equations on Schwarzchild manifold, Letters in Math. Phys.81, No3(2007)227-238.
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  6. Roland Donninger, Wilhelm Schlag, Avy Soffer, On pointwise decay of linear waves on a Schwarzschild black hole background Comm. Math. Phys. 309 (2012) No. 1, 51-86.
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  7. Roland Donninger, Wilhelm Schlag, Avy Soffer, A proof of Price’s Law on Schwarzschild black hole manifolds for all angular momenta, Advances in Mathematics Volume 226, Issue 1, 15 January 2011, Pages 484-540
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Soliton Dynamics

  1. A. Soffer and M. Weinstein, Multichannel Nonlinear Scattering Theory for Nonintegrable Equations, Comm. Math. Phys., 133, 1990, 119-146.
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  2. A. Soffer and M. Weinstein, Multichannel Nonlinear Scattering Theory for Nonintegrable Equations II, the Case of Anisotropic Potentials and Data, Journal of Differential Equations, 98 No. 2, 1992, 376-390.
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  3. A. Soffer, M. Weinstein, Selection of the ground state in the nonlinear Schrödinger equation, Rev. Math. Phys., 16, No.8 (2004), 977-1071.
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  4. I. Rodnianski, W. Schlag, A. Soffer, Asymptotic stability of CHANGE NEEDED N-solitons, submitted, (2003), (75+ pages).
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  5. V. Fleurov, A. Soffer, Nonlinear effects in tunneling escape in CHANGE NEEDED -body quantum systems, Europhysics Letters, 72, No.2 (2005), 287-293.
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  6. A. Soffer, M. Weinstein, Theory of Multidimensional Nonlinear Dispersive Waves: From Exact Results to Applications, Phys. Rev. Lett. 95 213905(2005).
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  7. G. Dekel, V. Fleurov, A. Soffer, C. Stucchio, Temporal dynamics of tunneling. Hydrodynamic approach, Physical Rev. A. 75 043617(2007).
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  8. A. Soffer, Soliton Dynamics and Scattering, International Congress of Mathematicians Vol III,(2006).459-471
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  9. A.Barak, O. Peleg, C. Stucchio, A.Soffer, M. Segev Observation of Soliton Tunneling Phenomena and Soliton Ejection, Phys. Rev. Lett. 100, 153901 (2008).
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  10. A. Soffer Geometric Characterization of Solitons, Comm. Partial Differential Equations 33 (2008), no. 10-12, 1953–1974
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  11. E. Cohen, S. Muenzel, J. Fleischer, V. Fleurov, A. Soffer Jet-like tunneling from a trapped vortex Physical Review A 88.4 (2013): 043833.
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Other

  1. N. Komarova, A. Soffer, Nonlinear waves in double-stranded DNA, Bull. Math. Biology, 67, No.4 (2005), 701-718.
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Nonlinear Waves

  1. J. Ginibre, A. Soffer and G. Velo, The Global Cauchy Problem for the Critical Nonlinear Wave Equation, Journal of Functional Analysis, 110, No. 1, 1992, 96-130.
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  2. A. Soffer, M. Weinstein, Resonances, Radiation Damping and Instability in Hamiltonian nonlinear wave equations, Inventiones mathematicae, 136, 1999, 9-74.
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  3. H. Lindblad, A. Soffer, A remark on long range scattering for the nonlinear Klein-Gordon equation, J. Hyperbolic Diff. Eqs., 2, No.1 (2005), 77-89.
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  4. H. Lindblad, A. Soffer, Asymptotic Completeness for the critical Klein-Gordon Equation, Lett. Math. Phys., Vol.3 (2005)249-258.
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  5. H. Lindblad, A. Soffer, Scattering and small data completeness for the critical nonlinear Schrödinger equation,Nonlinearity 19 (2006) 345-353
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  6. S. Fishman, Y. Krivolapov, A. Soffer, On the problem of dynamical localization in the nonlinear Schrödinger equation with a random potential, J. Stat. Phys. 131 (2008), no. 5, 843–865.
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  7. Juerg Froehlich, Zhou Gang, Avy Soffer Some Hamiltonian Models of Friction J. Math. Phys. 52 (2011) No.8, 083508.
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  8. S.Fishman, Y. Krivolapov, A. Soffer The Nonlinear Schrödinger Equation with a random potential: Results and Puzzles, Nonlinearity 25 (2012), no. 4,pages R53-R72 .(Solicited)
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  9. Juerg Froehlich, Zhou Gang, Avy Soffer Friction in a model of Hamiltonian Dynamics Comm. Math. Phys. 315, 401444 (2012).
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  10. S. Fishman, A. Soffer Multiscale Time Averaging, reloaded (2012), SIAM Journal of Math Analysis, 46(2), 13851405 (2014).
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  11. H Lindblad, A Soffer Scattering for the Klein-Gordon equation with quadratic and variable coefficient cubic nonlinearities Trans. AMS, to appear. arXiv preprint arXiv:1307.5882
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Manuscripts

  1. I.M. Sigal and A. Soffer, Asymptotic Completeness for Long Range 3-body Systems, (40 pages), preprint, Caltech 1987, (ftp://www.math.rutgers.edu/pub/soffer).
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Quantum Theory and Scattering

  1. I.M. Sigal and A. Soffer, The N -particle Scattering Problem-Asymptotic Completeness for Short Range Systems, Annals of Math., 126, 1987, 35-108.
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  2. I.M. Sigal and A. Soffer, Local Decay and Propagation Estimates for Time Dependent and Time Independent Hamiltonians, (50 pages), preprint, Princeton 1988,
    (ftp://www.math.rutgers.edu/pub/soffer).
  3. I.M. Sigal and A. Soffer, Long Range Many Body Scattering Asymptotic Clustering for Coulomb Type Potentials, Inventiones Mathematics, 99, 1990, 115-143.
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  4. A. Soffer, On the Many Body Problems in Quantum Mechanics, Méthodes Semiclassiques, Astérisque, 207, 1, 1992, 109-152.
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  5. I.M. Sigal and A. Soffer, Asymptotic Completeness for NEEDS CHANGEParticles Systems with Coulomb-type Interactions, Duke Math. J. 71, No. 1, 1993, 243-298.
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  6. I.M. Sigal and A. Soffer, Asymptotic Completeness of Particle Long Range Scattering, J. Am. Math. Soc., 7, No. 2, 1994, 307-334.
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  7. V. Bach, J. Fröhlich, I. M. Sigal, A. Soffer, Positive Commutators and Spectrum of Pauli-Fierz Hamiltonians of Atoms and Molecules, Comm. Math. Phys., 207, 1999, 557-587.
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  8. W. Hunziker, I. M. Sigal, A. Soffer, Minimal Velocity Bounds, Comm. PDE, 24, (1999), No. 11/12, 2279-2295.
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  9. I. Rodnianski, W. Schlag, A. Soffer, Dispersive analysis of charge transfer models, Communications on Pure and Applied Mathematics 58, Issue 2 (2005), 149-216.
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  10. Marius Beceanu, Avy Soffer The Schrödinger Equation with Potential in Rough Motion Comm. Partial Differential Equations 37 (2012), no. 6, 9691000
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Probability theory and statistical physics

  1. M. Schwartz and A. Soffer, An Exact Inequality for Random Systems Applications to Random Field, Phys. Rev. Lett., 55, 1985, 2499.
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  2. M. Schwartz and A. Soffer, Critical Correlation, Susceptibility Relations In Random Field Systems, Phys. Rev., B15 , Rapid Comm. 33, No. 3-4, 1986, 2059-2061.
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  3. E. Carlen and A. Soffer, Entropy Production by Block Spin Summation and Central Limit Theorems, Comm. Math. Phys. 140, No. 2, 1991, 339-371.
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  4. E. Carlen, A. Soffer, Propagation of Localization optimal entropy production and convergence rates for the centarl Limit Theorem submitted (2011), (22 pages).
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