Nghiem Nguyen Ph.D.

Publications | Journal Articles

Academic Journal

• Liu, C., Nguyen, N.V, Tian, R., Wang, Z.Q, (2025). On the stability of solitary-wave and ground-state solutions for the generalized BBM equation. Physica Scripta, doi: 10.1088/1402-4896/ae3260
• Nguyen, N.V, Brewer, B., (2025). Explicit synchronized solitary waves for some models for the interaction of long and short waves in dispersive media. Water Waves
• L., Nguyen, N.V, Wang, Z.Q, (2016). Orbital stability of spatially synchronized solitary waves of an m-coupled nonlinear Schrodinger system. Journal of Mathematical Physics
• Nguyen, N.V, Wang, Z.Q, (2016). Existence and stability of a two-parameter family of solitary waves for a 2-coupled nonlinear Schrodinger system. Discrete and Continuous Dynamical System A., 36:2, 1005-1021. doi: doi: 10.3934/dcds.2016.36.1005.
• D., Nguyen, N.V, S., (2016). The interaction of long and short waves in dispersive media. Journal of Physics A: Mathematical and Theoretical, 49, doi: The interaction of long and short waves in dispersive media Bernard Deconinck 1 , 3 , Nghiem V Nguyen 2 , 3 and Benjamin L Segal 1 , 3 1 Department of Applied Mathematics, University of Washington, Seattle, WA 98195- 3925, USA 2 Department of Mathematics and Statistics, Utah State University, Logan, UT 84322- 3900, USA Received 14 April 2016, revised 23 August 2016 Accepted for publication 31 August 2016 Published 21 September 2016 Abstract The KdV equation models the propagation of long waves in dispersive media, while the NLS equation models the dynamics of narrow-bandwidth wave packets consisting of short dispersive waves. A system that couples the two equations to model the interaction of long and short w aves is mathematically attractive and such a system has been studied over the l ast decades. We evaluate the validity of this system as a physical model, discussi ng two main problems. First, only the system coupling the linear Schrödinger equation with KdV has been derived in the literature. Second, the time variabl es appearing in the equations are of a different order. It appears that in the manuscripts that study the coupled NLS-KdV system, an assumption has been made that the coupled system can be derived, justifying its mathematical study. In fact , this is true even for the papers where the asymptotic derivation with the problems d escribed above is presented. In addition to discussing these inconsistencies, we p resent an alternative system describing the interaction of long and short waves. Keywords: water waves, Korteweg – de Vries, nonlinear Schrodinger 1. Introduction Considerable attention ( e.g. [ 2 – 4 , 8 , 9 , 14 ] ) has been devoted to the following system, which has become known as the cubic nonlinear Schrödinger – Korteweg – deVries ( NLS-KdV ) system: Journal of Physics A: Mathematical and Theoretical J. Phys. A: Math. Theor. 49 ( 2016 ) 415501 ( 10pp ) doi:10.1088 / 1751-8113 / 49 / 41 / 415501
• L., Nguyen, N.V, Wang, Z.Q, (2016). Existence and stability of solitary waves of an m-coupled nonlinear Schrodinger system. Journal of Mathematical Study, 49:2, 132-148. doi: doi: 10.4208/jms.v49n2.16.03
• Nguyen, N.V, (2014). Stability of solitary waves for the vector nonlinear Schrodinger equation in higher-order Sobolev spaces. Journal of Mathematical Analysis and Applications, 409, 946-962. doi: http://dx.doi.org/10.1016/j.jmaa.2013.07.050.
• Nguyen, N.V, Wang, Z.Q, Tian, R., (2014). Stability of traveling-wave solutions for a Schrodinger system with power-type nonlinearities. . Electronic Journal of Differential Equations, 2014:217, 1-16.
• Nguyen, N.V, (2014). Existence of periodic traveling-wave solutions for a nonlinear Schrodinger system: a topological approach. Topological Methods in Nonlinear Analysis. , 43:1, 129-155.
• Deconinck, B., Shiels, N., Nguyen, N.V, Tian, R., (2013). On the Spectral Stability of Soliton Solutions of the vector Nonlinear Schrodinger Equation. Journal of Physics A: Mathematical and Theoretical., 46:41, doi: doi:10.1088/1751-8113/46/41/415202
• Nguyen, N.V, Wang, Z.Q, (2013). Orbital stability of solitary waves of a 3-coupled nonlinear Schrodinger system. Journal of Nonlinear Analysis Series A: Theory, Methods & Applications. , 90, 1-26. doi: 10.1016/j.na.2013.05.027.
• Nguyen, N.V, Tian, R., Deconinck, B., Shiels, N., (2013). Global existence for a system of Schrodinger equations with power-type nonlinearities. , 54, 20. doi: 10.1063/1.4774149
• Chen, M., Nguyen, N.V, Sun, S., (2011). Existence of Solitary-Wave Solutions to Boussinesq Systems. Differential and Integral Equations, 24:9-10, 896-908.
• Nguyen, N.V, (2011). On the Orbital Stability of Solitary Waves for the 2-Coupled Nonlinear Schrodinger System. Communications in Mathematical Sciences, 9:4, 997-1012.
• Nguyen, N.V, Wang, Z.Q, (2011). Orbital Stability of Solitary Waves for a Nonlinear Schrodinger System. Advances in Differential Equations, 16:9-10, 977-1000.
• Chen, M., Nguyen, N.V, Sun, S., (2010). Solitary-wave Solutions to Boussinesq Systems with Large Surface Tension. Discrete and Continuous Dynamical Systems, 6:4, 1153-1184.
• Chen, M., Curtis, C.W, Deconinck, B., Lee, C.W, Nguyen, N.V, (2010). Spectral Stability of Stationary Solutions of a Boussinesq System Describing Long Waves in Dispersive Media. SIAM Journal on Applied Dynamical Systems, 9:3, 999-1018.
• Chen, H., Chen, M., Nguyen, N.V, (2007). Cnoidal Wave Solutions to Boussinesq Systems. , 20, 1443-1461.
• Albert, J.P, Bona, J.L, Nguyen, N.V, (2007). On the Stability of KdV Multi-Solitons. Diff. and Int. Equations, 20:8, 841-878.
• Bona, J., Liu, Y., Nguyen, N.V, (2004). Stability of Solitary Waves in Higher-Order Sobolev Spaces. Comm. in Math Sciences, 2, 35-52.
• Nguyen, N.V, A variational characterization of 2-soliton profiles for the KdV equation. Communications in Mathematical Sciences

An asterisk (*) at the end of a publication indicates that it has not been peer-reviewed.

Publications | Other

An asterisk (*) at the end of a publication indicates that it has not been peer-reviewed.