Related papers: Characteristic invariants and Darboux's method
One unusual property of dynamic systems, whose state is characterized by a set of scalar dynamic variables satisfying a system of differential equations of a general form, is considered. This property is related to the behavior of equations…
In this paper a hyperbolic system of partial differential equations for two-phase mixture flows with $N$ components is studied. It is derived from a more complicated model involving diffusion and exchange terms. Important features of the…
Developing an original idea of De Giorgi, we introduce a new and purely variational approach to the Cauchy Problem for a wide class of defocusing hyperbolic equations. The main novel feature is that the solutions are obtained as limits of…
We present a construction of a large class of Laplace invariants for linear hyperbolic partial differential operators of fairly general form and arbitrary order.
Some of the guiding problems in partially hyperbolic systems are the following: (1) Examples, (2) Properties of invariant foliations, (3) Accessibility, (4) Ergodicity, (5) Lyapunov exponents, (6) Integrability of central foliations, (7)…
Invariant ergodic measures for generalized Boole type transformations are studied using an invariant quasi-measure generating function approach based on special solutions to the Frobenius--Perron operator. New two-dimensional Boole type…
In this paper, we study diagonal hyperbolic systems in one space dimension. Based on a new gradient entropy estimate, we prove the global existence of a continuous solution, for large and non-decreasing initial data. We remark that these…
This article addresses linear hyperbolic partial differential equations with non-smooth coefficients and distributional data. Solutions are studied in the framework of Colombeau algebras of generalized functions. Its aim is to prove upper…
A new family of skew-symmetric solutions of the Jacobi partial differential equations for finite-dimensional Poisson systems is characterized and analyzed. Such family has some remarkable properties. In first place, it is defined for…
We introduce an approximation technique for nonlinear hyperbolic systems with sources that is invariant domain preserving. The method is discretization-independent provided elementary symmetry and skew-symmetry properties are satisfied by…
This paper is devoted to the study of hyperbolic systems of linear partial differential equations perturbed by a Brownian motion. The existence and uniqueness of solutions are proved by an energy method. The specific features of this class…
Darboux transformation is a powerful tool for the construction of new solvable models in quantum mechanics. In this article, we discuss its use in the context of physical systems described by $4\times4$ Dirac Hamiltonians. The general…
A new form of a binary Darboux transformation is used to generate analytical solutions of a nonlinear Liouville-von Neumann equation. General theory is illustrated by explicit examples.
A ``hybrid method'', dedicated to asymptotic coefficient extraction in combinatorial generating functions, is presented, which combines Darboux's method and singularity analysis theory. This hybrid method applies to functions that remain of…
In this paper hyperbolic partial differential equations with random coefficients are discussed. We consider the challenging problem of flux functions with coefficients modeled by spatiotemporal random fields. Those fields are given by…
We prove regularity estimates for time derivatives of a large class of nonlinear parabolic partial differential systems. This includes the instationary (symmetric) p-Laplace system and models for non Newtonien fluids of powerlaw or Carreau…
Classical Bianchi-Lie, Backlund and Darboux transformations are considered. Their generalizations for the dynamical systems are discussed. For the transformation being the generalization of the normal shift the special class of dynamical…
We propose a numerical method to solve general hyperbolic systems in any space dimension using forward Euler time stepping and continuous finite elements on non-uniform grids. The properties of the method are based on the introduction of an…
In this paper invariant subspace method has been employed for solving linear and non-linear fractional partial differential equations involving Caputo derivative. A variety of illustrative examples are solved to demonstrate the…
Integrable systems in low dimensions, constructed through the symmetry reduction method, are studied using phase portrait and variable separation techniques. In particular, invariant quantities and explicit periodic solutions are…