Sergey Leble's Books

The Dynamical Projectors Method

Hydro and Electrodynamics

By: Sergey Leble,Anna Perelomova

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The Dynamical Projectors Method

Hydro and Electrodynamics

By: Sergey Leble,Anna Perelomova

The dynamical projectors method proves to reduce a multicomponent problem to the simplest one-component problem with its solution determined by specific initial or boundary conditions. Its universality and application in many different physical problems make it particularly useful in hydrodynamics, electrodynamics, plasma physics, and boundary layer problems. A great variety of underlying mechanisms are included making this book useful for those working in wave theory, hydrodynamics, electromagnetism, and applications. "The authors developed a universal and elegant tool – dynamical projector method. Using this method for very complicated hydro-thermodynamic and electrodynamics problem settings, they were able to get a lot of interesting analytical results in areas where before often just numerical methods were applicable." —L. A. Bordag, University of Applied Sciences Zittau/Görlitz, Zittau, Germany "The book is intended for professionals working in various fields of linear and nonlinear mathematical physics, partial differential equations and theoretical physics. The book is written clearly, and in my opinion, its material will be useful and easy to understand for professionals and for students familiar with ordinary and partial differential equations." —Sergey Dobrokhotov, Russian Academy of Sciences, Moscow, Russia

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Page Count

398

Publisher

CRC Press

Published Date

ISBN 10

1351107976

ISBN 13

9781351107976

Waveguide Propagation of Nonlinear Waves

Impact of Inhomogeneity and Accompanying Effects

By: Sergey Leble

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Waveguide Propagation of Nonlinear Waves

Impact of Inhomogeneity and Accompanying Effects

By: Sergey Leble

This book addresses the peculiarities of nonlinear wave propagation in waveguides and explains how the stratification depends on the waveguide and confinement. An example of this is an optical fibre that does not allow light to pass through a density jump. The book also discusses propagation in the nonlinear regime, which is characterized by a specific waveform and amplitude, to demonstrate so-called solitonic behaviour. In this case, a wave may be strongly localized, and propagates with a weak change in shape. In the waveguide case there are additional contributions of dispersion originating from boundary or asymptotic conditions. Offering concrete guidance on solving application problems, this essentially (more than twice) expanded second edition includes various aspects of guided propagation of nonlinear waves as well as new topics like solitonic behaviour of one-mode and multi-mode excitation and propagation and plasma waveguides, propagation peculiarities of electromagnetic waves in metamaterials, new types of dispersion, dissipation, electromagnetic waveguides, planetary waves and plasma waves interaction.The key feature of the solitonic behaviour is based on Coupled KdV and Coupled NS systems. The systems are derived in this book and solved numerically with the proof of stability and convergence. The domain wall dynamics of ferromagnetic microwaveguides and Bloch waves in nano-waveguides are also included with some problems of magnetic momentum and charge transport.

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Page Count

298

Publisher

Springer

Published Date

ISBN 10

3030226522

ISBN 13

9783030226527

A Dressing Method in Mathematical Physics

By: Evgeny V. Doktorov,Sergey B. Leble

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A Dressing Method in Mathematical Physics

By: Evgeny V. Doktorov,Sergey B. Leble

This monograph systematically develops and considers the so-called "dressing method" for solving differential equations (both linear and nonlinear), a means to generate new non-trivial solutions for a given equation from the (perhaps trivial) solution of the same or related equation. Throughout, the text exploits the "linear experience" of presentation, with special attention given to the algebraic aspects of the main mathematical constructions and to practical rules of obtaining new solutions.

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Page Count

413

Publisher

Springer Science & Business Media

Published Date

ISBN 10

1402061404

ISBN 13

9781402061400

Surveys in Applied Mathematics

Volume 2

By: Mark I. Freidlin,Sergey Gredeskul,John K. Hunter,Andrew Marchenko,Leonid Pastur

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Surveys in Applied Mathematics

Volume 2

By: Mark I. Freidlin,Sergey Gredeskul,John K. Hunter,Andrew Marchenko,Leonid Pastur

Volume 2 offers three in-depth articles covering significant areas in applied mathematics research. Chapters feature numerous illustrations, extensive background material and technical details, and abundant examples. The authors analyze nonlinear front propagation for a large class of semilinear partial differential equations using probabilistic methods; examine wave localization phenomena in one-dimensional random media; and offer an extensive introduction to certain model equations for nonlinear wave phenomena.

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Page Count

297

Publisher

Springer Science & Business Media

Published Date

ISBN 10

1461519918

ISBN 13

9781461519911

Waveguide Propagation of Nonlinear Waves

Impact of Inhomogeneity and Accompanying Effects

By: Sergey Leble

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Waveguide Propagation of Nonlinear Waves

Impact of Inhomogeneity and Accompanying Effects

By: Sergey Leble

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Solve jigsaw puzzle

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Page Count

298

Publisher

Springer

Published Date

ISBN 10

3030226522

ISBN 13

9783030226527

The Dynamical Projectors Method

Hydro and Electrodynamics

By: Sergey Leble,Anna Perelomova

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The Dynamical Projectors Method

Hydro and Electrodynamics

By: Sergey Leble,Anna Perelomova

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Solve jigsaw puzzle

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Page Count

398

Publisher

CRC Press

Published Date

ISBN 10

1351107976

ISBN 13

9781351107976

A Dressing Method in Mathematical Physics

By: Evgeny V. Doktorov,Sergey B. Leble

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A Dressing Method in Mathematical Physics

By: Evgeny V. Doktorov,Sergey B. Leble

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Solve jigsaw puzzle

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Page Count

413

Publisher

Springer Science & Business Media

Published Date

ISBN 10

1402061404

ISBN 13

9781402061400

Book's by Sergey Leble

The Dynamical Projectors Method

The Dynamical Projectors Method

Waveguide Propagation of Nonlinear Waves

Waveguide Propagation of Nonlinear Waves

A Dressing Method in Mathematical Physics

A Dressing Method in Mathematical Physics

Surveys in Applied Mathematics

Surveys in Applied Mathematics

Waveguide Propagation of Nonlinear Waves

Waveguide Propagation of Nonlinear Waves

The Dynamical Projectors Method

The Dynamical Projectors Method

A Dressing Method in Mathematical Physics

A Dressing Method in Mathematical Physics

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