منابع مشابه
Refraction of dispersive shock waves
We study a dispersive counterpart of the classical gas dynamics problem of the interaction of a shock wave with a counter-propagating simple rarefaction wave often referred to as the shock wave refraction. The dispersive shock wave (DSW) refraction due to its head-on collision with the centred rarefaction wave (RW) is considered in the frameworks of the one-dimensional defocusing nonlinear Schr...
متن کاملDispersive Hydrodynamics: the Mathematics of Dispersive Shock Waves and Applications
Dispersive hydrodynamics is the domain of applied mathematics and physics concerned with fluid motion in which internal friction, e.g., viscosity, is negligible relative to wave dispersion. In conservative media such as superfluids, optical materials, and water waves, nonlinearity has the tendency to engender wavebreaking that is mitigated by dispersion. The mathematical framework for such medi...
متن کاملNonlinear Dispersive Waves on Trees
We investigate the well-posedness of a class of nonlinear dispersive waves on trees, in connection with the mathematical modeling of the human cardiovascular system. Specifically, we study the Benjamin-Bona-Mahony (BBM) equation, also known as the regularized long wave equation, posed on finite trees, together with standard junction and terminal boundary conditions. We prove that the Cauchy pro...
متن کاملDispersive and Diffusive-Dispersive Shock Waves for Nonconvex Conservation Laws
We consider two physically and mathematically distinct regularization mechanisms of scalar hyperbolic conservation laws. When the flux is convex, the combination of di↵usion and dispersion are known to give rise to monotonic and oscillatory traveling waves that approximate shock waves. The zero-di↵usion limits of these traveling waves are dynamically expanding dispersive shock waves (DSWs). A r...
متن کاملInstability of nonlinear dispersive solitary waves
We consider linear instability of solitary waves of several classes of dispersive long wave models. They include generalizations of KDV, BBM, regularized Boussinesq equations, with general dispersive operators and nonlinear terms. We obtain criteria for the existence of exponentially growing solutions to the linearized problem. The novelty is that we dealt with models with nonlocal dispersive t...
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ژورنال
عنوان ژورنال: The Journal of the Acoustical Society of America
سال: 1966
ISSN: 0001-4966
DOI: 10.1121/1.2143490