Related papers: Characteristic invariants and Darboux's method
The aim of the present paper is to study the existence, uniqueness and some other properties of solutions of a certain partial dynamic integrodifferential equations. The Banach fixed point theorem and certain fundamental inequality with…
In this paper we shall study differential equations in the complex domain. The method of indeterminate coefficients and the majorant method lead to a proof of the existence and uniqueness of meromorphic solution of differential equations.…
In this article the unique solution of the Cauchy problem is founded by the Riemann method. Some relations for given here confluent hypergeometric functions of two and three variables are used.
The paper studies the complex differentiable functions of double argument and their properties, which are similar to the properties of the holomorphic functions of complex variable: the Cauchy formula, the hyperbolic harmonicity, the…
This paper extends, to a class of systems of semi-linear hyperbolic second order PDEs in three variables, the geometric study of a single nonlinear hyperbolic PDE in the plane as presented in [Anderson I.M., Kamran N., Duke Math. J. 87…
The general approach to chain equations derivation for the function generated by a Miura transformation analog is developing to account evolution (second Lax equation) and illustrated for Sturm-Liouville differential and difference…
A new procedure for the global construction of the Casimir invariants and Darboux canonical form for finite-dimensional Poisson systems is developed. This approach is based on the concept of matrix congruence and can be applied without the…
We study ergodic properties of partially hyperbolic systems whose central direction is mostly contracting. Earlier work of Bonatti, Viana about existence and finitude of physical measures is extended to the case of local diffeomorphisms.…
We show that for a hyperbolic system of hydrodynamic type admitting n symmetries, there exists a coordinate system in which the generator of the system and all the symmetries are diagonal.
We study the inverse problem of deducing the dynamical characteristics (such as the potential field) of large systems from kinematic observations. We show that, for a class of steady-state systems, the solution is unique even with…
This paper considers one-dimensional equations of acoustics equations of inhomogeneous media and the system of gas dynamics equations with constant entropy. Using the Riemann approach, the gas dynamics equations are reduced to a…
Using a theorem of partial differential equations, we present a general way of deriving the conserved quantities associated with a given classical point mechanical system, denoted by its Hamiltonian. Some simple examples are given to…
Using exhaustion method and finite differences a new method to solve system of partial differential equations and is presented. This method allows design algorithm to solve linear and nonlinear systems in irregular domains. Applying this…
Recent work in dynamical systems theory has shown that many properties that are associated with irreversible processes in fluids can be understood in terms of the dynamical properties of reversible, Hamiltonian systems. That is,…
We prove that 1) diagonal systems of hydrodynamic type are Darboux integrable if and only if the corresponding systems for commuting flows are Darboux integrable, 2) systems for commuting flows are Darboux integrable if and only if the…
In this article we study generalizations of the inhomogeneous Burgers equation. First at the operator level, in the sense that we replace classical differential derivations by operators with certain properties, and then we increase the…
Invariant conditions for conformable fractional problems of the calculus of variations under the presence of external forces in the dynamics are studied. Depending on the type of transformations considered, different necessary conditions of…
Two new approaches to solving first-order quasilinear elliptic systems of PDEs in many dimensions are proposed. The first method is based on an analysis of multimode solutions expressible in terms of Riemann invariants, based on links…
We present an extension of the Piecewise Parabolic Method to special relativistic fluid dynamics in multidimensions. The scheme is conservative, dimensionally unsplit, and suitable for a general equation of state. Temporal evolution is…
The numerical method of Kahan applied to quadratic differential equations is known to often generate integrable maps in low dimensions and can in more general situations exhibit preserved measures and integrals. Computerized methods based…