Related papers: Symmetric hyperbolic systems and shock waves
We show that horizontally symmetric water waves are traveling waves. The result is valid for the Euler equations, and is based on a general principle that applies to a large class of nonlinear partial differential equations, including some…
An extension of the finite and infinite Lie groups properties of complex numbers and functions of complex variable is proposed. This extension is performed exploiting hypercomplex number systems that follow the elementary algebra rules. In…
The Hyperspherical Harmonics basis, without a previous symmetrization step, is used to calculate binding energies of the nuclear A=6 systems using a version of the Volkov potential acting only on s-wave. The aim of this work is to…
A set of travelling wave solutions to a hyperbolic generalization of the convection-reaction-diffusion is studied by the methods of local nonlinear alnalysis and numerical simulation. Special attention is paid to displaying appearance of…
Symmetric quantum states are fascinating objects. They correspond to multipartite systems that remain invariant under particle permutations. This symmetry is reflected in their compact mathematical characterisation but also in their unique…
Superposition of explicit (analytic) monotone non-increasing shock waves for the KdV-Burgers equation is studied, modelled numerically and graphically presented. Initial profile chosen as a sum of two such shock waves gradually transforms…
We present a brief survey of the spectral theory and dynamics of infinite volume asymptotically hyperbolic manifolds. Beginning with their geometry and examples, we proceed to their spectral and scattering theories, dynamics, and the…
The use of dynamical symmetries or spectrum generating algebras for the solution of the nuclear many-body problem is reviewed. General notions of symmetry and dynamical symmetry in quantum mechanics are introduced and illustrated with…
In the following paper we will consider Navier-Stokes problem and it's interpretation by hyperbolic waves, focusing on wave propagation. We will begin with solution for linear waves, then present problem for non-linear waves. Later we will…
Two geometrical well-posed hyperbolic formulations of general relativity are described. One admits any time-slicing which preserves a generalized harmonic condition. The other admits arbitrary time-slicings. Both systems have only the…
This work studies a macroscopic traffic flow model driven by a system of nonlinear hyperbolic partial differential equations. Using Lie symmetry analysis, we determine the infinitesimal generators and construct an optimal system of…
Physical theories grounded in mathematical symmetries are an essential component of our understanding of a wide range of properties of the universe. Similarly, in the domain of machine learning, an awareness of symmetries such as rotation…
We derive a new hyperbolic model describing the propagation of internal waves in a stratified shallow water with a non-hydrostatic pressure distribution. The construction of the hyperbolic model is based on the use of additional…
Lie symmetry group method is applied to study Newtonian incompressible fluid's equations flow in turbulent boundary layers. The symmetry group and its optimal system are given, and group invariant solutions associated to the symmetries are…
A method is suggested for treating those complicated physical problems for which exact solutions are not known but a few approximation terms of a calculational algorithm can be derived. The method permits one to answer the following rather…
The Hyperbolic Nonlinear Schrodinger equation (HypNLS) arises as a model for the dynamics of three-dimensional narrowband deep water gravity waves. In this study, the Petviashvili method is exploited to numerically compute bi-periodic…
This is a survey on the analytic theory of linear wave equations on globally hyperbolic Lorentzian manifolds. There is no claim of originality.
Group theory is used in many textbooks of contemporary physics. However, electromagnetic community often considers group theory as an "exotic" tool. Graduate and postgraduate textbooks on electromagnetics and electrodynamics usually do not…
In this paper, we propose quasilinearization methods that convert nonlocal fully-nonlinear parabolic systems into the nonlocal quasilinear parabolic systems. The nonlocal parabolic systems serve as important mathematical tools for modelling…
We show the continuity of the flow map for quasilinear symmetric hyperbolic systems with general right--hand sides in different functional setting, including weighted Sobolev spaces $H_{s,\delta}$. An essential tool to achieve the…