Vadim Vereschagin - Academia.edu (original) (raw)

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Papers by Vadim Vereschagin

A century-old history of calculation of asymptotics for solutions to Painlevé equations (usually ... more A century-old history of calculation of asymptotics for solutions to Painlevé equations (usually denoted Pj, j=1,2,...,6) as their variable x tends to infinity was started by pioneer works by Painlevé, Gambier and Boutroux [1]. In 1980-1981 papers by Jimbo, Miwa and Flashka, Newell [2] initiated the

arXiv: Exactly Solvable and Integrable Systems, 1997

Problem of asymptotic description for global solutions to the six Painleve equations was investig... more Problem of asymptotic description for global solutions to the six Painleve equations was investigated. Elliptic anzatzes and appropriate modulation equations were written out.

Nonlinear integrable models with two spatial and one temporal variables: Kadomtsev-Petviashvili e... more Nonlinear integrable models with two spatial and one temporal variables: Kadomtsev-Petviashvili equation and two-dimensional Toda lattice are investigated on the subject of correct formulation for boundary problem that can be solved within the framework of the Inverse Scattering Problem method. It is shown that there exists a large set of integrable boundary problems and various curves can be chosen as boundary contours for them. We develop a method for obtaining explicit solutions to integrable boundary problems and its effectiveness is illustrated by series of examples.

Fuel and Energy Abstracts, Oct 18, 2010

Spatially two-dimensional Toda lattice is examined in the aspect of correct formulation of bounda... more Spatially two-dimensional Toda lattice is examined in the aspect of correct formulation of boundary problems that can be solved within the scheme of the Inverse Scattering Method. It is shown that there exists a large set of integrable boundary problems and various curves can be chosen as boundaries for those problems. Explicit solutions are presented for problems on closed and unclosed curves taken as boundary contours.

Eprint Arxiv Hep Th 9409026, Sep 1, 1994

Nonlinear integrable models with two spatial and one temporal variables: Kadomtsev-Petviashvili e... more Nonlinear integrable models with two spatial and one temporal variables: Kadomtsev-Petviashvili equation and two-dimensional Toda lattice are investigated on the subject of correct formulation for boundary problem that can be solved within the framework of the Inverse Scattering Problem method. It is shown that there exists a large set of integrable boundary problems and various curves can be chosen as boundary contours for them. We develop a method for obtaining explicit solutions to integrable boundary problems and its effectiveness is illustrated by series of examples.

Problem of asymptotic description for global solutions to the six Painleve equations was investig... more Problem of asymptotic description for global solutions to the six Painleve equations was investigated. Elliptic anzatzes and appropriate modulation equations were written out.

Eprint Arxiv Solv Int 9707004, Jul 7, 1997

The connection between modulated Riemann surface of genus one and solution to Volterra lattice th... more The connection between modulated Riemann surface of genus one and solution to Volterra lattice that tends to constants at infinity is studied. The main term of asymptotics for large time of solution to the mentioned Cauchy problem is written out.

Physica D: Nonlinear Phenomena, 1996

The main subject of the paper is the so-called Discrete Painlev\'e-1 Equation (DP1). Solutio... more The main subject of the paper is the so-called Discrete Painlev\'e-1 Equation (DP1). Solutions of the DP1 are classified under criterion of their behavior while argument tends to infinity. The appropriate theorems of existence are proved.

Theoretical and Mathematical Physics, 2009

Nonlinear Analysis: Theory, Methods & Applications, 1992

Physica D: Nonlinear Phenomena, 1996

A century-old history of calculation of asymptotics for solutions to Painlevé equations (usually ... more A century-old history of calculation of asymptotics for solutions to Painlevé equations (usually denoted Pj, j=1,2,...,6) as their variable x tends to infinity was started by pioneer works by Painlevé, Gambier and Boutroux [1]. In 1980-1981 papers by Jimbo, Miwa and Flashka, Newell [2] initiated the

arXiv: Exactly Solvable and Integrable Systems, 1997

Problem of asymptotic description for global solutions to the six Painleve equations was investig... more Problem of asymptotic description for global solutions to the six Painleve equations was investigated. Elliptic anzatzes and appropriate modulation equations were written out.

Nonlinear integrable models with two spatial and one temporal variables: Kadomtsev-Petviashvili e... more Nonlinear integrable models with two spatial and one temporal variables: Kadomtsev-Petviashvili equation and two-dimensional Toda lattice are investigated on the subject of correct formulation for boundary problem that can be solved within the framework of the Inverse Scattering Problem method. It is shown that there exists a large set of integrable boundary problems and various curves can be chosen as boundary contours for them. We develop a method for obtaining explicit solutions to integrable boundary problems and its effectiveness is illustrated by series of examples.

Fuel and Energy Abstracts, Oct 18, 2010

Spatially two-dimensional Toda lattice is examined in the aspect of correct formulation of bounda... more Spatially two-dimensional Toda lattice is examined in the aspect of correct formulation of boundary problems that can be solved within the scheme of the Inverse Scattering Method. It is shown that there exists a large set of integrable boundary problems and various curves can be chosen as boundaries for those problems. Explicit solutions are presented for problems on closed and unclosed curves taken as boundary contours.

Eprint Arxiv Hep Th 9409026, Sep 1, 1994

Nonlinear integrable models with two spatial and one temporal variables: Kadomtsev-Petviashvili e... more Nonlinear integrable models with two spatial and one temporal variables: Kadomtsev-Petviashvili equation and two-dimensional Toda lattice are investigated on the subject of correct formulation for boundary problem that can be solved within the framework of the Inverse Scattering Problem method. It is shown that there exists a large set of integrable boundary problems and various curves can be chosen as boundary contours for them. We develop a method for obtaining explicit solutions to integrable boundary problems and its effectiveness is illustrated by series of examples.

Problem of asymptotic description for global solutions to the six Painleve equations was investig... more Problem of asymptotic description for global solutions to the six Painleve equations was investigated. Elliptic anzatzes and appropriate modulation equations were written out.

Eprint Arxiv Solv Int 9707004, Jul 7, 1997

The connection between modulated Riemann surface of genus one and solution to Volterra lattice th... more The connection between modulated Riemann surface of genus one and solution to Volterra lattice that tends to constants at infinity is studied. The main term of asymptotics for large time of solution to the mentioned Cauchy problem is written out.

Physica D: Nonlinear Phenomena, 1996

The main subject of the paper is the so-called Discrete Painlev\'e-1 Equation (DP1). Solutio... more The main subject of the paper is the so-called Discrete Painlev\'e-1 Equation (DP1). Solutions of the DP1 are classified under criterion of their behavior while argument tends to infinity. The appropriate theorems of existence are proved.

Theoretical and Mathematical Physics, 2009

Nonlinear Analysis: Theory, Methods & Applications, 1992

Physica D: Nonlinear Phenomena, 1996