Publications of Stephanos Venakides

Papers Published

  1. N. Ptitsyna, S. P. Shipman, and S. Venakides, Fano resonance of waves in periodic slabs, Proceedings of the 12th International Conference on Mathematical Methods in Electrodynamic Theory (MMET08 Odesa) (2008) 73-78 (2008)
  2. X. G. Peralta, Y. Toyama, M. S. Hutson, R. Montague, S. Venakides, D. P. Kiehart and G. S. Edwards, Resiliency, coordination, and synchronization of dorsal closure during Drosophila morphogenesis, Biophysical Journal, vol. 92 (April, 2007), pp. 2583-2596
  3. A. Tovbis, S. Venakides, X. Zhou, Semiclassical Focusing Nonlinear Schrödinger Equation I: Inverse scattering map and its evolution for radiative initial data, International Mathematics Research Notices, vol. 2007 no. Article ID rnm094, 54 pages. doi:10. (2007)
  4. R. Buckingham, A. Tovbis, S. Venakides, X. Zhou, The semiclassical focusing nonlinear Schroedinger equation, in "Recent Advances in Nonlinear Partial Differentila Equations and Applications'', Proceedings of Symposia in Applied Mathematics, edited by L.L. Bonilla, A. Carpio, J.M. Vega, S. Venakides, vol. 65, (2007), pp. 47-80, American Mathematical Society, ISBN 978-0-8218-4211-9
  5. R. Buckingham, S. Venakides, Long-time asymptotics of the nonlinear {S}chr\"odinger equation shock problem, Communications on Pure and Applied Mathematics, vol. 60 no. 9 (2007), pp. 1349--1414, ISSN 0010-3640
  6. A. Tovbis, S. Venakides, X. Zhou, On the long time limit of semiclassical (zero dispersion limit) solutions of the focusing Nonlinear Schroedinger Equation: Pure radiation case., vol. 59 no. 10 (2006), pp. 1379 - 1432
  7. S. Shipman, S. Venakides, Resonant transmission near nonrobust periodic slab modes, Phys. Rev. E, vol. 71 (2005), pp. 026611(1-10)
  8. A. Tovbis, S. Venakides, X Zhou, On semiclassical (zero dispersion limit) solutions of the focusing nonlinear {S}chr\"odinger equation, Communications on Pure and Applied Mathematics, vol. 57 no. 7 (2004), pp. 877--985, ISSN 0010-3640
  9. Stephen Shipman and Stephanos Venakides, Resonance and bound states in photonic crystal slabs, SIAM J. Appl. Math., vol. 64 no. 1 (2003), pp. 322-342
  10. M. Shane Hutson, Yoichiro Tokutake, Ming-Shien Chang, James W. Bloor, Stephanos Venakides, Daniel P. Kiehart, and Glenn S. Edwards, Forces for Morphogenesis Investigated with Laser Microsurgery and Quantitative Modeling, Science, vol. 300 (2003), pp. 145-149
  11. M.A. Haider, S.P. Shipman and S. Venakides, Boundary-integral calculations of two-dimensional electromagnetic scattering in infinite photonic crystal slabs: Channel defects and resonances, SIAM Journal on Applied Mathematics, vol. 62, (2002), pp. 2129-2148
  12. El, G. A.; Krylov, A. L.; Venakides, S.,, Unified approach to KdV modulations, Comm. Pure Appl. Math. 54, no 10, (2001), pp. 1243-1270.
  13. El, G.A.; Krylov, A.L.; Molchanov, S.A.; Venakides, S., Soliton turbulence as a thermodynamic limit of stochastic soliton lattices. In Advances in nonlinear mathematics and science., Physica D 152/153 (2001), 653--664
  14. A. Georgieva, T. Kriecherbauer, Stephanos Venakides, 1:2 Resonance Mediated Second Harmonic Generation in a 1-d Nonlinear Discrete Periodic Medium, SIAM J. Appl. Math, vol 61 No 5 (2001) 1802-1815
  15. Alexander Tovbis, Stephanos Venakides, The Eigenvalue Problem for the Focusing Nonlinear Schroedinger Equation: New Solvable Cases, Physica D, vol. 146, (2000), pp. 150-164
  16. S. Venakides, M. Haider, V. Papanicolaou, Boundary Integral Calculations of 2-d Electromagnetic Scattering by Photonic Crystal Fabry-Perot Structures, SIAM J. Appl. Math. vol. 60/5, (2000), pp. 1636-1706
  17. P. Deift, T. Kriecherbauer, K. T-R McLaughlin, S. Venakides, X. Zhou, Uniform Asymptotics for Polynomials Orthogonal with respect to Varying Exponential Weights and Applications to Universality Questions in Random Matrix Theory, CPAM vol. 52, (1999), pp. 1335-1425
  18. A. Georgieva, T. Kriecherbauer, Stephanos Venakides, Wave Propagation and Resonance in a 1-d Nonlinear Discrete Periodic Medium, SIAM J. Appl. Math., vol. 60/1, (1999), pp. 272-294
  19. P.J. Cheng, Stephanos Venakides, X. Zhou, Long-time Asymptotics for the Pure Radiation Solution of the Sine-Gordon Equation, Comm. in PDE, vol. 24(7-8), (1999), pp. 1195-1262
  20. M.M. Beaky, J.B. Burke, H.O. Everitt, M.A Haider, S. Venakides, Two Dimensional Photonic Crystal Fabry-Perot Resonators with Lossy Dielectrics, IEEE Transactions on Microwave Theory, vol. 47 No. 9 (1999) pp. 2085-2091
  21. P. Deift, T. Kriecherbauer, K. T-R McLaughlin,S. Venakides, X. Zhou, Strong Asymptotics of Orhtogonal Polynomials with Respect to Exponential Weights, CPAM, vol.52 (1999) 1491-1552.
  22. A. M. Filip, S. Venakides, Existence and Modulation of Traveling Waves in Particle Chains, CPAM, Vol 51, 1998, 693-736.
  23. M. McDonald, S. Venakides, Renormalization of the Tau Function for Integrable Systems: A Model Problem, CPAM, Vol 51, 1998, 937-966.
  24. P. Deift, S. Venakides, X. Zhou, An Extension of the Method of Steepest Descent for Riemann-Hilbert Problems: The Small Dispersion Limit of the Korteweg-de Vries (KdV) Equation, Proc. Ntl. Acad. Sc. USA, vol. 95, Jan 1998, 450-454.
  25. P. Deift, S. Venakides, X. Zhou, New Results in the Small-Dispersion KdV by an Extension of the Method of Steepest Descent for Riemann-Hilbert Problems, IMRN, 1997, N0. 6, 285-299.
  26. L.L. Bonilla. M. Kindelan, M. Moscoso, S. Venakides, Periodic Generation and Propagation of Traveling Fronts in dc Voltage Biased Semiconductor Superlattices, SIAM J. Appl. Math., Vol. 57, Number 6, 1997, 1588-1614
  27. P. Deift, T. Kriecherbauer, K. T-R McLaughlin,S. Venakides, X. Zhou, Asymptotics of Polynomials Orthogonal with Respect to Varying Exponential Weights, IMRN, 1997 No 16, pp. 759-782
  28. P. Deift, T. Kriecherbauer, S. Venakides, Forced Lattice Vibrations Part II, Comm. Pure Appl. Math. 48, 1995, 1251-1298.
  29. P. Deift, T. Kriecherbauer, S. Venakides, Forced Lattice Vibrations Part I, Comm. Pure Appl. Math. 48,1995, 1187-1250.
  30. L. L. Bonilla, F. Higuera, S. Venakides, The Stability of the Steady State of the Gunn Oscillator, SIAM J. Appl. Math. vol. 54, No 6, (1994), pp. 1521-1541.
  31. P. Deift, S. Venakides, X. Zhou, The Collisionless Shock Region for the Long Time Behavior of the Solutions of the KdV Equation, CPAM. vol. 47, (1994), pp. 199-206.
  32. T. Zhang, S. Venakides, Periodic Limit of Inverse Scattering, CPAM vol. 46 (1993), pp. 819-865.
  33. P. D. Lax, C. D. Levermore, S. Venakides, The Generation and Propagation of Oscillations in Dispersive IVP's and their Limiting Behavior, Important Developments in Soliton Theory 1980--1990}, T. Fokas and V.E. Zakharov eds., Springer-Verlag, Berlin (1992).
  34. S. Venakides, P. Deift, R. Oba, The Toda shock problem, CPAM vol 44 (1991), pp. 1171-1242.
  35. S. Venakides, The Korteweg-de Vries equation with small dispersion: Higher order Lax-Levermore theory, CPAM vol. 43 (1990), pp. 335-361.
  36. M. Reed, S. Venakides, J. J. Blum, Approximate travelling waves in linear reaction-hyperbolic equations, SIAP. 50, No 1 (1990), pp. 167-180. .
  37. S. Venakides, The continuum limit of Theta functions, CPAM, vol. 42, (1989) pp. 711-728.
  38. S. Venakides, The Infinite Period Limit of the Inverse Formalism for Periodic Potentials, CPAM, vol. 41, (1988) pp. 3-17.
  39. S. Venakides, The small dispersion limit of the Korteweg-de Vries equation, Proceedings of the Conference at M.S.R.I., in Berkeley in honor of P.D. Lax's 60th birthday, (editors A. J. Chorin, A. J. Majda) (1987) pp. 295-336.
  40. S. Venakides, The zero dispersion limit of the Korteweg-de Vries equation with periodic initial data, AMS Transactions, vol. 301 (1987), pp. 189-226.
  41. S. Venakides, The solution of completely integrable systems in the continuum limit of the spectral data, IMA Proceedings, vol. 2, (1986) pp. 337-356..
  42. S. Venakides, Long-time asymptotics of the Korteweg-de Vries equation, AMS Transactions 293 #1 (1986), pp. 411-419..
  43. S. Venakides, The generation of modulated wavetrains in the solution of the Korteweg-de Vries Equation, CPAM. 38, (1985), pp. 883-909..
  44. S. Venakides, The zero-dispersion limit of the Korteweg-de Vries equation with non-trivial reflection coefficient, Comm. Pure and Appl. Math. 38, pp. 125-155, 1985.

Papers Submitted

  1. A. Tovbis and S. Venakides, Determinant form of modulation equations for the semiclassical focusing Nonlinear Schr\" odinger equation., International Mathematics Research Notices IMRN (2008)
  2. W.R. Lefew, S. Venakides, D.J. Gauthier, Accurate description of optical precursors and their relation to weak-field coherent optical transients, Phys. Rev. Lett. (2007)