Nghiem V. Nguyen

Department of Mathematics and Statistics,
Office # AnSc 201,
Utah State University,
Phone: (435) 797-2819
Email: nghiem(dot)nguyen(at)usu(dot)edu


Research Interests

Partial Differential Equations, Nonlinear Evolution Equations, Fluid Mechanics, Nonlinear Waves.


Publications

Stability of solitary waves in higher-order Sobolev spaces, with J. Bona and Y. Liu, Communications in Mathematical Sciences, Vol 2, No 1, pp 35-52 (2004).

Cnoidal wave solutions to Boussinesq systems, with Hongqiu Chen and Min Chen, Nonlinearity, Vol 20, pp 1443-1461 (2007).

On the stability of KdV multi-solitons, with John Albert and Jerry Bona, Differential and Integral Equations, Vol 20, No. 8, pp 841-878 (2007).

Solitary-wave solutions to Boussinesq systems with large surface tension, with Min Chen and Shu-ming Sun, Discrete and Continuous Dynamical Systems A, Vol 26, No 4, pp 1153-1184 (2010). Special issue on recent progress on Partial Differential Equations modeling fluids and complex fluids.

Spectral stability of stationary solutions of a Boussinesq system describing long waves in dispersive media, with M. Chen, C. Curtis, B. Deconinck and C. Lee, SIAM Journal on Applied Dynamical Systems, Vol 9, No 3, pp 999-1018 (2010).

Existence of traveling-wave solutions to Boussinesq systems, with Min Chen and Shu-ming Sun, Differential and Integral Equations, Vol 24, No 9-10, pp 896-908 (2011).

On the orbital stability of solitary waves for the 2-coupled nonlinear Schrodinger system, Communications in Mathematical Sciences, Vol 9, No 4, pp 997-1012 (2011).

Orbital stability of solitary waves for a nonlinear Schrodinger system, with Zhi-Qiang Wang, Advances in Differential Equations, Vol 16, No 9-10, pp 977-1000 (2011).

Orbital stability of solitary waves of a 3-coupled nonlinear Schrodinger system, with Zhi-Qiang Wang, Journal of Nonlinear Analysis Series A: Theory, Methods & Applications, Vol 90, pp 1-26 (2013); doi: 10.1016/j.na.2013.05.027.

Global existence for a system of Schrodinger equations with power-type nonlinearities with B. Deconinck, N. Sheils and R. Tian, Journal of Mathematical Physics, Vol 54, No 1, 011503 (2013); doi: 10.1063/1.4774149.

On the spectral stability of soliton solutions of the vector nonlinear Schrodinger equation with B. Deconinck, N. Sheils and R. Tian, Journal of Physics A: Mathematical and Theoretical, Vol 46, No 41 (2013), 415202, http://dx.doi.org/10.1088/1751-8113/46/41/415202.

Existence of periodic traveling-wave solutions for a nonlinear Schrodinger system: a topological approach, Topological Methods in Nonlinear Analysis, Vol 43, No 1, pp 129-155 (2014).

Stability of solitary waves for the vector nonlinear Schrodinger equation in higher-order Sobolev spaces, Journal of Mathematical Analysis and Applications, Vol 409, 946-962 (2014), http://dx.doi.org/10.1016/j.jmaa.2013.07.050.

Stability of traveling-wave solutions for a Schrodinger system with power-type nonlinearities with Rushun Tian and Zhi-Qiang Wang, Electronic Journal of Differential Equations, Vol 2014, No 217, pp 1-16 (2014).

Existence and stability of a two-parameter family of solitary waves for a 2-coupled nonlinear Schrodinger system with Zhi-Qiang Wang, Discrete and Continuous Dynamical System A, Vol 36, No. 2, pp 1005-1021 (2016); doi: 10.3934/dcds.2016.36.1005.

Orbital stability of spatially synchronized solitary waves of an m-coupled nonlinear Schrodinger system, with Chuangye Liu and Zhi-Qiang Wang, Journal of Mathematical Physics, Vol 57, 101501 (2016); doi: 10.1063/1.4964255.

Existence and stability of solitary waves of an m-coupled nonlinear Schrodinger system, with Chuangye Liu and Zhi-Qiang Wang, Journal of Mathematical Study, Vol 49, No 2 (2016) 132-148; doi: 10.4208/jms.v49n2.16.03.

The interaction of long and short waves in dispersive media, with Bernard Deconinck and Benjamin L. Segal, Journal of Physics A: Mathematical and Theoretical, Vol 49 (2016) 415501, http://dx.doi.org/10.1088/1751-8113/49/41/415501.

Orbital stability of spatially synchronized solitary waves of Schrodinger system with power-type nonlinearities, with Chuangye Liu, Journal of Nonlinear and Convex Analysis, Vol 18, No 8, pp 1459-1483 (2017), Special Issue in Honor of the 65th Birthday of Norimichi Hirano.

Some models for the interaction of long and short waves in dispersive media. Part I: Derivation, with Chuangye Liu, Water Waves, 2, pp 327-359 (2020), https://doi.org/10.1007/s42286-020-00038-6

A variational characterization of 2-soliton profiles for the KdV equation, with John Albert, submitted to Transactions of the American Mathematical Society.

 

Teaching

Fall 2020

 Spring 2021