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34
The quantum hydrodynamic model for semiconductor devices
 SIAM Journal on Applied Mathematics
, 1994
"... Abstract. The classical hydrodynamic equations can be extended to include quantum effects by incorporating the first quantum corrections. These quantum corrections are O(h2). The full threedimensional quantum hydrodynamic (QHD) model is derived for the first time by a moment expansion of the Wigner ..."
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Cited by 84 (9 self)
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dimensional QHD transport equations are mathematically classified as having two Schr6dinger modes, two hyperbolic modes, and one parabolic mode. The onedimensional steadystate QHD equations are discretized in conservation form using the second upwind method. Simulations of a resonant tunneling diode
A Localized modes in a chain with nonlinear onsite potential
 PHYSICS LETTERS A
, 1993
"... Localized modes are analysed for a chain with nonlinear onsite potential using an approximation based on the discrete nonlinear Schr0dinger equation. It is pointed out that such localized modes exist in the parameter domains where the system displays modulational instability. Otherwise, nonlinear m ..."
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Cited by 1 (0 self)
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Localized modes are analysed for a chain with nonlinear onsite potential using an approximation based on the discrete nonlinear Schr0dinger equation. It is pointed out that such localized modes exist in the parameter domains where the system displays modulational instability. Otherwise, nonlinear
Evolution of Nonlinear Alfvén Waves in Streaming Inhomogeneous Plasmas
, 1999
"... Nonlinear evolution equation for Alfvn waves, propagating in streaming plasmas with nonuniform densities and inhomogeneous magnetic fields, is obtained by using the reductive perturbation technique. The governing equation is a modified derivative nonlinear Schr6dinger (MDNLS) equation. Numerical ..."
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Cited by 1 (0 self)
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Nonlinear evolution equation for Alfvn waves, propagating in streaming plasmas with nonuniform densities and inhomogeneous magnetic fields, is obtained by using the reductive perturbation technique. The governing equation is a modified derivative nonlinear Schr6dinger (MDNLS) equation. Numerical
MULTIPLE SOLUTIONS OF·A STATIONARY NONHOMOGENEOUS ONEDIMENSIONAL NONLINEAR SCHRODINGER EQUATION
"... In this work we study the multiplicity of solutions for a stationary nonhomogeneous problem associated to the nonlinear onedimensional Schr6dinger Equation.. We prove the existence of a number ko E IN such that for every j> ko there exist at least two solutions of the Dirichlet problem with exac ..."
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In this work we study the multiplicity of solutions for a stationary nonhomogeneous problem associated to the nonlinear onedimensional Schr6dinger Equation.. We prove the existence of a number ko E IN such that for every j> ko there exist at least two solutions of the Dirichlet problem
Ramaninduced optical shocks in nonlinear fibers
, 1992
"... It is demonstrated that the stimulated Raman scattering in optical fibers supports kink solitons (shocks) not only in the recently considered case of anomalous dispersion but also in the normaldispersion regime. In both cases there is a family of the kinks depending on an arbitrary (positive) wave ..."
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. As is well known, propagation of short pulses in optical fibers is governed by the nonlinear Schr6dinger (NLS) equation.1,2 However, several higherorder effects become important for femtosecond optical pulses. The pulse evolution is described by the generalized NLS equation, which includes these higher
Quantum molecular dynamics: A new algorithm for linear and nonlinear electron transport in disordered materials
, 1990
"... Quantum molecular dynamics (QMD) simulations provide the realtime dynamics of electrons and ions through numerical solutions of the timedependent Schrödinger and Newton equations, respectively. With this technique it is possible to go beyond the structural aspects to study electron dynam ..."
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Cited by 1 (0 self)
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dynamics, including linear and nonlinear electron transport, in materials at finite temperatures. The solution of the timedependent Schrödinger equation for the electron wave function is obtained by a spectral method, which for bulk systems is implemented with discrete fast Fourier (FFT
Mathematical Physics 9 SpringerVerlag 1996 Dynamic Stability of Vortex Solutions of GinzburgLandau and Nonlinear
, 1995
"... Abstract: The dynamic stability of vortex solutions to the GinzburgLandau and nonlinear Schr6dinger equations is the basic assumption of the asymptotic particle plus field description of interacting vortices. For the GinzburgLandau dynamics we prove that all vortices are asymptotically nonlinearly ..."
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Abstract: The dynamic stability of vortex solutions to the GinzburgLandau and nonlinear Schr6dinger equations is the basic assumption of the asymptotic particle plus field description of interacting vortices. For the GinzburgLandau dynamics we prove that all vortices are asymptotically
Nonlinear Waves In WeaklyCoupled Lattices
, 2013
"... We consider existence and stability of breather solutions to discrete nonlinear SchrÃ¶dinger (dNLS) and discrete KleinGordon (dKG) equations near the anticontinuum limit, the limit of the zero coupling constant. For sufficiently small coupling, discrete breathers can be uniquely extended from the ..."
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We consider existence and stability of breather solutions to discrete nonlinear SchrÃ¶dinger (dNLS) and discrete KleinGordon (dKG) equations near the anticontinuum limit, the limit of the zero coupling constant. For sufficiently small coupling, discrete breathers can be uniquely extended from
Wave Occurrence Using LargeScale PhaseResolved Nonlinear Simulations
"... It is challenging to obtain accurate predictions of ocean surface wavefield evolutions due to several complex dynamic processes involved, including nonlinear wave interaction, wave breaking and wind forcing, and also wave interactions with currents and bottom bathymetry. With fast computational alg ..."
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occurrence are investigated based on the simulated wavefields. The SNOW results are compared to available wave basin experiments and predictions from linear theory and approximate nonlinearSchr6dingerequation (NLS) type models. SNOW
OVER A VARIABLE DEPTH
, 1981
"... A theoretical study of water waves and current over variable depth is performed. Multiplescalesanalysis is used to derive the equation governing the evolution of a 1D wave packet. The current is assumed to be colinear with the wave number vector and with the depth gradient. The equation which is f ..."
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is found is a cubic Schr6dinger equation with nonconstant coefficients. Some analytical properties of this equation are studied. The equation is then solved numerically and the effect of current and depth variation on the propagation of a solitary wave is studied.
Results 11  20
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34