Related papers: Symmetries and Riemann Invariants
We review how an algebraic formulation for the dynamics of a physical system allows to describe a reduction procedure for both classical and quantum evolutions.
The theory of plasma physics offers a number of nontrivial examples of partial differential equations, which can be successfully treated with symmetry methods. We propose three different examples which may illustrate the reciprocal…
In this paper, we study two systems with a time-variable coefficient and general time-gradually-degenerate damping. More explicitly, we construct the Riemann solutions to the time-variable coefficient Zeldovich approximation and…
Bathymetry reconstruction is an important problem in various fields, including oceanography and environmental monitoring. This paper presents a Bayesian inference approach to reconstructing bathymetries from point measurements of the water…
The renormalization group (RG) method is extended for global asymptotic analysis of discrete systems. We show that the RG equation in the discretized form leads to difference equations corresponding to the Stuart-Landau or Ginzburg-Landau…
We study Manakov-Santini equation, starting from Lax-Sato form of associated hierarchy. The waterbag reduction for Manakov-Santini hierarchy is introduced. Equations of reduced hierarchy are derived.We construct new coordinates transforming…
We consider model order reduction of parameterized Hamiltonian systems describing nondissipative phenomena, like wave-type and transport dominated problems. The development of reduced basis methods for such models is challenged by two main…
Some iterative techniques are defined to solve reversible inverse problems and a common formulation is explained. Numerical improvements are suggested and tests validate the methods.
The article explores the acoustic equations in inhomogeneous media and the linearized shallow water equations. Two methods for integrating these equations are proposed. The first method is based on the of the Laplace cascade method, while…
Governing equations of dissipative generalized solid mechanics are derived by thermodynamic methods in the Piola-Kirchhoff framework using the Liu procedure. The isotropic small strain case is investigated in more detail. The connection to…
We review and slightly improve the known k-polysymplectic Marsden--Weinstein reduction theory by removing some technical conditions on k-polysymplectic momentum maps by developing a theory of affine Lie group actions for k-polysymplectic…
An alternative approach to solving the Landau-Khalatnikov problem on one-dimensional stage of expansion of hot hadronic matter created in collisions of high-energy particles or nuclei is suggested. Solving the relativistic hydrodynamics…
Based on the Lie symmetry method, we investigate a Feynman-Kac formula for the classical geometric mean reversion process, which effectively describing the dynamics of short-term interest rates. The Lie algebra of infinitesimal symmetries…
The multichannel generalization of the theory of spectral, scattering and decay control is presented. New universal algorithms of construction of complex quantum systems with given properties are suggested. Particularly, transformations of…
An application of a quantum wave impedance method for a study of quantum-mechanical systems which con\-tain singular zero-range potentials is considered. It was shown how to reformulate the problem of an investigation of mentioned systems…
We give a pedagogical introduction to the Generalized Hydrodynamic approach to inhomogeneous quenches in integrable many-body quantum systems. We review recent applications of the theory, focusing in particular on two classes of problems:…
In Newtonian and relativistic hydrodynamics the Riemann problem consists of calculating the evolution of a fluid which is initially characterized by two states having different values of uniform rest-mass density, pressure and velocity.…
In this paper we revise two classical examples of Relativistic Hydrodynamics in order to illustrate in detail the numerical methods commonly used in fluid dynamics, specifically those designed to deal with shocks, which are based on a…
We study quantum statistical inference tasks of hypothesis testing and their canonical variations, in order to review relations between their corresponding figures of merit---measures of statistical distance---and demonstrate the crucial…
We consider the inverse problem of reconstructing inhomogeneities by performing a finite number of scattering measurements of acoustic type in the time-harmonic setting. We set up the reconstruction as a fully discrete variational problem…