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Publications of Stephanos Venakides    :recent first  combined  bibtex listing:

Papers Published

  1. 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.
  2. S. Venakides, The generation of modulated wavetrains in the solution of the Korteweg-de Vries Equation, CPAM. 38, (1985), pp. 883-909..
  3. S. Venakides, Long-time asymptotics of the Korteweg-de Vries equation, AMS Transactions 293 #1 (1986), pp. 411-419..
  4. S. Venakides, The solution of completely integrable systems in the continuum limit of the spectral data, IMA Proceedings, vol. 2, (1986) pp. 337-356..
  5. S. Venakides, The zero dispersion limit of the Korteweg-de Vries equation with periodic initial data, AMS Transactions, vol. 301 (1987), pp. 189-226.
  6. 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.
  7. S. Venakides, The Infinite Period Limit of the Inverse Formalism for Periodic Potentials, CPAM, vol. 41, (1988) pp. 3-17.
  8. S. Venakides, The continuum limit of Theta functions, CPAM, vol. 42, (1989) pp. 711-728.
  9. M. Reed, S. Venakides, J. J. Blum, Approximate travelling waves in linear reaction-hyperbolic equations, SIAP. 50, No 1 (1990), pp. 167-180. .
  10. S. Venakides, The Korteweg-de Vries equation with small dispersion: Higher order Lax-Levermore theory, CPAM vol. 43 (1990), pp. 335-361.
  11. S. Venakides, P. Deift, R. Oba, The Toda shock problem, CPAM vol 44 (1991), pp. 1171-1242.
  12. 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).
  13. T. Zhang, S. Venakides, Periodic Limit of Inverse Scattering, CPAM vol. 46 (1993), pp. 819-865.
  14. 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.
  15. 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.
  16. P. Deift, T. Kriecherbauer, S. Venakides, Forced Lattice Vibrations Part I, Comm. Pure Appl. Math. 48,1995, 1187-1250.
  17. P. Deift, T. Kriecherbauer, S. Venakides, Forced Lattice Vibrations Part II, Comm. Pure Appl. Math. 48, 1995, 1251-1298.
  18. 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
  19. 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.
  20. 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
  21. 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.
  22. M. McDonald, S. Venakides, Renormalization of the Tau Function for Integrable Systems: A Model Problem, CPAM, Vol 51, 1998, 937-966.
  23. A. M. Filip, S. Venakides, Existence and Modulation of Traveling Waves in Particle Chains, CPAM, Vol 51, 1998, 693-736.
  24. 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.
  25. 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
  26. 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
  27. Alexander Tovbis, Stephanos Venakides, The Eigenvalue Problem for the Focusing Nonlinear Schroedinger Equation: New Solvable Cases, Physica D, vol. 146, (2000), pp. 150-164
  28. 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
  29. 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
  30. 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
  31. El, G. A.; Krylov, A. L.; Venakides, S.,, Unified approach to KdV modulations, Comm. Pure Appl. Math. 54, no 10, (2001), pp. 1243-1270.
  32. 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
  33. 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
  34. 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
  35. 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
  36. 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
  37. 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 [MR2044068 (2005c:35269)]
  38. S. Shipman, S. Venakides, Resonant transmission near nonrobust periodic slab modes, Phys. Rev. E, vol. 71 (2005), pp. 026611(1-10)
  39. 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 [MR2248894]  [abs]
  40. 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 [MR2337507]  [abs]
  41. 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)  [abs]
  42. 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
  43. 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  [abs]
  44. 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) [arXiv:0804.3148]  [abs]

Papers Published

  1. W. R. Lefew, S. Venakides, D. Gauthier, Accurate description of optical precursors and their relation to weak-field coherent optical transients, Phys. Rev. A., vol. 79 (2009), pp. 063842
  2. A. Tovbis, S. Venakides, Determinant form of the complex phase function of the steepest descent analysis of Riemann-Hilbert problems and its application to the focusing Nonlinear Schr\" odinger Equation, Int. Math. Res. Notices,, vol. 2009 (2009), pp. 2056-2080
  3. A. T. Layton1, Y. Toyama, G-Q Yang, G. S. Edwards, D. P. Kiehart, S. Venakides, Drosophila Morphogenesis:Tissue Force Laws and the Modeling of Dorsal Closure, HFSPHFSP (Human Frontier Science Program) Journal Published online 2009 December 15. doi: 10.2976/1.3266062., vol. 3 no. 6 (2009), pp. 441-460, HFSP  [abs]
  4. A. Tovbis, S. Venakides, Nonlinear steepest descent asymptotics for semiclassical limit of integrable systems: Continuation in the parameter space, Comm. Math. Phys., vol. 295 no. 1 (2010), pp. 139-160  [abs]
  5. A. Tovbis, S. Venakides, Semiclassical Limit of the Scattering Transform for the Focusing Nonlinear Schrödinger Equation, Int Math Res Notices, vol. 2012 no. 10 (2012), pp. 2212-2271 (doi:10.1093/imrn/rnr092.)  [abs]
  6. S. Shipman, S. Venakides, An exactly solvable model for nonlinear resonant scattering, Nonlinearity, vol. 25 no. 9 (2012), pp. 2473-2501 (doi:10.1088/0951-7715/25/9/2473.)  [abs]