## 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)

- Y.-H. Kuo, L. Lee, and G. Lyng, Analysis and development of compact finite difference schemes with optimized numerical dispersion relations, arXiv:1409.3535.

### Papers

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

- J. Hendricks, J. Humpherys, G. Lyng, and K. Zumbrun,

Stability of viscous weak detonation waves for Majda's model.

*Journal of Dynamics and Differential Equations*, accepted (2015).

Preprint: arXiv:1307.4416. - B. Barker, J. Humpherys, G. Lyng, and K. Zumbrun,

Viscous hyperstabilization of detonation waves in one space dimension.

*SIAM Journal on Applied Mathematics*, accepted (2015).

Preprint: arXiv:1311.6417. - Y. Kim, L. Lee, and G. Lyng,

The Wentzel-Kramers-Brillouin approximation of semiclassical eigenvalues of the Zakharov-Shabat problem.

*Journal of Mathematical Physics*,**55**(2014): 083516, 18pages.

Preprint: arXiv:1310.4145. - J. Humpherys, G. Lyng, and K. Zumbrun,

Stability of viscous detonations for Majda's model.

*Physica D*,**259**(2013): 63 - 80.

Preprint: arXiv:1301.1260. - 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*,**73**(2015): 1 - 21.

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. D. Lyng, Semiclassical soliton ensembles for the focusing nonlinear Schrödinger equation: recent developments, in "Nonlinear Wave Equations: Analytic and Computational Techniques," 91 - 108,
*Contemporary Mathematics,***635**, American Mathematical Society, Providence, RI, 2015. *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.