Zobrazeno 1 - 10
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pro vyhledávání: '"Kosovtsov, Yu. N."'
Autor:
Kosovtsov, Yu. N.
In this report the emphasis is on an alternative representation of the Magnus series by proper operator (matrix) exponential solutions to differential equations (systems), both linear and nonlinear ODEs and PDEs. The main idea here is in \emph{exact}
Externí odkaz:
http://arxiv.org/abs/2406.08574
Autor:
Kosovtsov, Yu. N.
The paper establishes conditions under which there are exact linear representations of nonlinear partial differential equations (Cauchy problems). By introducing a certain linear operator $A$, it is shown that under these conditions there are three e
Externí odkaz:
http://arxiv.org/abs/2308.12081
Autor:
Kosovtsov, Yu. N.
Based on Leray's formulation of the Navier-Stokes equations and the conditions of the exact linear representation of the nonlinear problem found in this paper, a compact explicit expression for the exact operator solution of the Navier-Stokes equatio
Externí odkaz:
http://arxiv.org/abs/2209.06587
Autor:
Kosovtsov, Yu. N.
The compact explicit expressions for formal exact operator solutions to Cauchy problem for sufficiently general systems of nonlinear differential equations (ODEs and PDEs) in the form of chronological operator exponents are given. The variant of exac
Externí odkaz:
http://arxiv.org/abs/0910.3923
Autor:
Kosovtsov, Yu. N.
In the first part of planned series of papers the formal general solutions to selection of 80 examples of different types of second order nonlinear PDEs in two independent variables with constant parameters are given. The main goal here is to show on
Externí odkaz:
http://arxiv.org/abs/0801.4081
Autor:
Kosovtsov, Yu. N.
In present paper we propose seemingly new method for finding solutions of some types of nonlinear PDEs in closed form. The method is based on decomposition of nonlinear operators on sequence of operators of lower orders. It is shown that decompositio
Externí odkaz:
http://arxiv.org/abs/0704.0072
Autor:
Kosovtsov, Yu. N.
Selection of 25 examples from extensive nontrivial families for different types of nonlinear PDEs and their formal general solutions are given. The main goal here is to show on examples the types of solvable PDEs and what their general solutions look
Externí odkaz:
http://arxiv.org/abs/math-ph/0609003
Autor:
Kosovtsov, Yu. N.
The aim of this paper is twofold. First, we obtain the explicit exact formal solutions of differential equations of different types in the form with Dyson chronological operator exponents. This allows us to deal directly with the solutions to the equ
Externí odkaz:
http://arxiv.org/abs/math-ph/0409035
Autor:
Kosovtsov, Yu. N.
We describe a solving semi-decision method based on examination of the rational structures of the generalized integrating factors of first-order ODEs. We propose a conjecture that for some family of equations of the type dy/dx=P(x,y)/Q(x,y), with P a
Externí odkaz:
http://arxiv.org/abs/math-ph/0211069
Autor:
Kosovtsov, Yu. N.
In present paper we propose an approach based on examination of the structure of the general solution of equations of the type dy/dx=P(x,y)/Q(x,y), with P and Q polynomials only in y. Under the term structure we mean the dependency character of solut
Externí odkaz:
http://arxiv.org/abs/math-ph/0207032