Gregory D. Lyng

Research

Research Interests

Nonlinear waves, existence & stability of traveling waves, Evans-function techniques, conservation & balance laws, gas dynamics, shock waves, combustion, integrable equations.

Preprint(s)

• J. Humpherys, G. Lyng, and K. Zumbrun, Stability of viscous detonations for Majda's model, arXiv:1301.1260.

Papers

Note: Preprints posted on arXiv (where available) are preliminary versions and may differ from the final, published versions.

• L. Lee and G. Lyng
  A second look at the Gaussian semiclassical soliton ensemble for the focusing nonlinear Schrödinger equation.
  Physics Letters A, 377 (2013): 1179 - 1188.
  Preprint: arXiv:1211.1988.
• N. Anderson, A. Lindgren, and G. Lyng
  Computing the refined stability condition.
  Quarterly of Applied Mathematics, accepted (2013).
  Preprint: arXiv:1207.4101.
• L. Lee, G. Lyng, and I. Vankova
  The Gaussian semiclassical soliton ensemble and numerical methods for the focusing nonlinear Schrödinger equation.
  Physica D, 241 (2012): 1767 - 1781.
  Preprint: arXiv:1207.0824.
• J. Humpherys, G. Lyng, and K. Zumbrun
  Spectral stability of ideal-gas shock layers.
  Archive for Rational Mechanics and Analysis, 194 (2009): 1029 - 1079.
  Preprint: arXiv:0712.1299
• G. Lyng, M. Raoofi, B. Texier, and K. Zumbrun
  Pointwise Green function bounds and stability of combustion waves.
  Journal of Differential Equations, 233 (2007): 654 - 698.
  Preprint: arXiv:math/0607064
• N. Costanzino, H. K. Jenssen, G. Lyng, and M. Williams
  Existence and stability of curved multidimensional detonation fronts.
  Indiana University Mathematics Journal, 56 (2007): 1405 - 1462.
  
• G. Lyng and P. D. Miller
  The N-soliton of the focusing nonlinear Schrödinger equation for N large.
  Communications on Pure and Applied Mathematics, 60 (2007): 951 - 1026.
  Preprint: arXiv:nlin/0508007
• H. K. Jenssen, G. Lyng, and M. Williams
  Equivalence of low-frequency stability conditions for multidimensional detonations in three models of combustion.
  Indiana University Mathematics Journal, 54 (2005): 1 - 64.
  
• G. Lyng and K. Zumbrun
  One-dimensional stability of viscous strong detonation waves.
  Archive for Rational Mechanics and Analysis, 173, (2004), no. 2, 213 - 277.
  
• G. Lyng and K. Zumbrun
  A stability index for detonation waves in Majda's model for reacting flow.
  Physica D, 194 (2004), no. 1-2, 1 - 29.
  

Conference Proceedings, Reports, Appendices

• G. Lyng, K. Zumbrun, and H. K. Jenssen, Stability of detonation waves, EQUADIFF 2003, 517-519 World Sci. Publ., Hackensack, New Jersey, 2005.
• H. K. Jenssen, G. Lyng, and M. Williams, Low frequency stability of planar multi-D detonations, Oberwolfach Reports, Volume 1, Issue 2, 2004, report No. 18/2004, 927-928.
• H. K. Jenssen and G. Lyng, Evaluation of the Lopatinski condition for gas dynamics, appendix to K. Zumbrun, Stability of large-amplitude shock waves of compressible Navier-Stokes equations, In: Handbook of Mathematical Fluid Dynamics III, S. Friedlander and D. Serre eds., North-Holland, Amsterdam, 2004.

Slides from Selected Talks

• The semiclassical limit of the focusing nonlinear Schrödinger equation: overview & recent results, PDE Seminar, Indiana University: Bloomington, IN: 2012
• Spectral Stability of Ideal-Gas Shock Layers, Rocky Mountain Mathematics Consortium Summer School, Laramie, WY: 2010.
• The large-N limit of N-solitons for the focusing NLS equation: the secondary caustic, AMS-SMM Seventh International Meeting, Zacatecas, Mexico: 2007.