Browsing by Author "Wong, Yau-Shu"

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Numerical computations for long-wave short-wave interaction equations in semi-classical limit
(2008-10-01)
Chang, Qianshun
;
Wong, Yau-Shu
;
Lin, Chi-Kun
;
應用數學系
;
Department of Applied Mathematics
This paper presents and compares various numerical techniques for the long-wave short-wave interaction equations. In addition to the standard explicit, implicit schemes and the spectral methods, a novel scheme SRK which is based on a time-splitting approach combined with the Runge-Kutta method is presented. We demonstrate that not only the SRK scheme is efficient compared to the split step spectral methods, but it can apply directly to problems with general boundary conditions. The conservation properties of the numerical schemes are discussed. Numerical simulations are reported for case studies with different types of initial data. The present study enhances our understanding of the behavior of nonlinear dispersive waves in the semi-classical limit. (C) 2008 Elsevier Inc. All rights reserved.
Quasineutral Limit of the Schrodinger-Poisson System in Coulomb Gauge
(2011)
Lin, Chi-Kun
;
Wong, Yau-Shu
;
Wu, Kung-Chien
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應用數學系
;
數學建模與科學計算所(含中心)
The zero Debye length asymptotic of the Schrodinger-Poisson system in Coulomb gauge for ill-prepared initial data is studied. We prove that when the scaled Debye length lambda -> 0, the current density defined by the solution of the Schrodinger-Poisson system in the Coulomb gauge converges to the solution of the rotating incompressible Euler equation plus a fast singular oscillating gradient vector field.
Zero-dispersion limit of the short-wave-long-wave interaction equations
(2006-09-01)
Lin, Chi-Kun
;
Wong, Yau-Shu
;
應用數學系
;
Department of Applied Mathematics
The purpose of this paper is to study the zero-dispersion limit of the water wave interaction equations which arise in modelling surface waves in the present of both gravity and capillary modes. This topic is also of interest in plasma physics. For the smooth solution, the limiting equation is given by the compressible Euler equation with a nonlocal pressure caused by the long wave. For weak solution, when the coupling coefficient lambda is small order of epsilon, lambda = o(epsilon), the wave map equation is derived and the scattering sound wave is shown to satisfy a linear wave equation. (c) 2006 Elsevier Inc. All rights reserved.