scholarly journals Traveling waves for quantum hydrodynamics with nonlinear viscosity

2021 ◽  
Vol 493 (1) ◽  
pp. 124503
Author(s):  
Corrado Lattanzio ◽  
Delyan Zhelyazov
Keyword(s):  
Traveling Waves ◽  
Quantum Hydrodynamics ◽  
Nonlinear Viscosity

scholarly journals Spectral analysis of dispersive shocks for quantum hydrodynamics with nonlinear viscosity

2021 ◽  
pp. 1-29
Author(s):  
Corrado Lattanzio ◽  
Delyan Zhelyazov
Keyword(s):  
Traveling Wave ◽  
Point Spectrum ◽  
Traveling Wave Solutions ◽  
Maximum Modulus ◽  
Negative Real Part ◽  
Sufficient Condition ◽  
Winding Number ◽  
Quantum Hydrodynamics ◽  
Nonlinear Viscosity ◽  
The Stability

In this paper, we investigate spectral stability of traveling wave solutions to 1D quantum hydrodynamics system with nonlinear viscosity in the [Formula: see text], that is, density and velocity, variables. We derive a sufficient condition for the stability of the essential spectrum and we estimate the maximum modulus of eigenvalues with non-negative real part. In addition, we present numerical computations of the Evans function in sufficiently large domain of the unstable half-plane and show numerically that its winding number is (approximately) zero, thus giving a numerical evidence of point spectrum stability.

NON-MONOTONIC TRAVELING WAVES IN VAN DER WAALS FLUIDS

2005 ◽  
Vol 03 (04) ◽  
pp. 419-446 ◽  
Author(s):  
N. BEDJAOUI ◽  
C. CHALONS ◽  
F. COQUEL ◽  
P. G. LeFLOCH
Keyword(s):  
Traveling Waves ◽  
Traveling Wave ◽  
Van Der Waals ◽  
Traveling Wave Solutions ◽  
Left Hand ◽  
Wave Solutions ◽  
Nonlinear Viscosity ◽  
Classical Trajectories ◽  
Parameter Values ◽  
Van Der Waals Fluids

We investigate the existence and properties of traveling wave solutions for the hyperbolic-elliptic system of conservation laws describing the dynamics of van der Waals fluids. The model is based on a constitutive equation of state containing two inflection points and incorporates nonlinear viscosity and capillarity terms. A global description of the traveling wave solutions is provided. We distinguish between classical and non-classical trajectories and, for the latter, the existence and properties of kinetic functions is investigated. An earlier work in this direction (cf. [4]) was restricted to dealing with one inflection point only. Specifically, given any left-hand state and any shock speed (within some admissible range), we prove the existence of a non-classical traveling wave for a sequence of parameter values representing the ratio of viscosity and capillarity. Our analysis exhibits a surprising lack of monotonicity of traveling waves. The behavior of these non-classical trajectories is also investigated numerically.

Double-Diffusive Convection in Traveling Waves in the Iodate−Sulfite System Explained

1996 ◽  
Vol 100 (40) ◽  
pp. 16209-16212 ◽  
Author(s):  
John A. Pojman ◽  
Andrea Komlósi ◽  
Istvan P. Nagy
Keyword(s):  
Traveling Waves ◽  
Double Diffusive Convection ◽  
Diffusive Convection ◽  
Double Diffusive

Existence of traveling waves in Fermi–Pasta–Ulam–type systems on a 2D–lattice

2021 ◽  
Vol 252 (4) ◽  
pp. 453-462
Author(s):  
Sergiy Mykolayovych Bak ◽  
Galyna Mykolayivna Kovtonyuk
Keyword(s):  
Traveling Waves ◽  
Type Systems

Evolution of nonlinear stationary formations in a quantum plasma at finite temperature

2021 ◽  
Vol 76 (4) ◽  
pp. 329-347
Author(s):  
Swarniv Chandra ◽  
Chinmay Das ◽  
Jit Sarkar
Keyword(s):  
Finite Temperature ◽  
Acoustic Waves ◽  
Quantum Plasma ◽  
Quantum Hydrodynamics ◽  
Stationary Structure ◽  
Gradual Evolution ◽  
Layer Structures ◽  
Model Equations ◽  
Electron Acoustic ◽  
Shock Fronts

Abstract In this paper we have studied the gradual evolution of stationary formations in electron acoustic waves at a finite temperature quantum plasma. We have made use of Quantum hydrodynamics model equations and obtained the KdV-Burgers equation. From here we showed how the amplitude modulated solitons evolve from double layer structures through shock fronts and ultimately converging into solitary structures. We have studied the various parametric influences on such stationary structure and also showed how the gradual variations of these parameter affect the transition from one form to another. The results thus obtained will help in the generation and structure of the structures in their respective domain. Much of the experiments on dense plasma will benefit from the parametric study. Further we have studied amplitude modulation followed by a detailed study on chaos.

Sign in / Sign up

Export Citation Format

Share Document