The Complex WKB Method for Nonlinear Equations: I: Linear Theory (Paperback)
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The Complex WKB Method for Nonlinear Equations: I: Linear Theory (Paperback) (2012)
DE PB NW RP
ISBN: 9783034896696 bzw. 3034896697, in Deutsch, Springer Basel, Switzerland, Taschenbuch, neu, Nachdruck.
Von Händler/Antiquariat, The Book Depository EURO [60485773], London, United Kingdom.
Language: English Brand New Book ***** Print on Demand *****.This book deals with asymptotic solutions of linear and nonlinear equa- tions which decay as h ---+ 0 outside a neighborhood of certain points, curves and surfaces. Such solutions are almost everywhere well approximated by the functions cp(x) exp{iS(x)/h}, x E 1R3, where S(x) is complex, and ImS(x) ~ O. When the phase S(x) is real (ImS(x) = 0), the method for obtaining asymp- totics of this type is known in quantum mechanics as the WKB-method. We preserve this terminology in the case ImS(x) ~ 0 and develop the method for a wide class of problems in mathematical physics. Asymptotics of this type were constructed recently for many linear prob- lems of mathematical physics; certain specific formulas were obtained by differ- ent methods (V. M. Babich [5 -7], V. P. Lazutkin [76], A. A. Sokolov, 1. M. Ter- nov [113], J. Schwinger [107, 108], E. J. Heller [53], G. A. Hagedorn [50, 51], V. N. Bayer, V. M. Katkov [21], N. A. Chernikov [35] and others). However, a general (Hamiltonian) formalism for obtaining asymptotics of this type is clearly required; this state of affairs is expressed both in recent mathematical and physical literature. For example, the editors of the collected volume [106] write in its preface: One can hope that in the near future a computational pro- cedure for fields with complex phase, similar to the usual one for fields with real phase, will be developed. Softcover reprint of the original 1st ed. 1994.
Language: English Brand New Book ***** Print on Demand *****.This book deals with asymptotic solutions of linear and nonlinear equa- tions which decay as h ---+ 0 outside a neighborhood of certain points, curves and surfaces. Such solutions are almost everywhere well approximated by the functions cp(x) exp{iS(x)/h}, x E 1R3, where S(x) is complex, and ImS(x) ~ O. When the phase S(x) is real (ImS(x) = 0), the method for obtaining asymp- totics of this type is known in quantum mechanics as the WKB-method. We preserve this terminology in the case ImS(x) ~ 0 and develop the method for a wide class of problems in mathematical physics. Asymptotics of this type were constructed recently for many linear prob- lems of mathematical physics; certain specific formulas were obtained by differ- ent methods (V. M. Babich [5 -7], V. P. Lazutkin [76], A. A. Sokolov, 1. M. Ter- nov [113], J. Schwinger [107, 108], E. J. Heller [53], G. A. Hagedorn [50, 51], V. N. Bayer, V. M. Katkov [21], N. A. Chernikov [35] and others). However, a general (Hamiltonian) formalism for obtaining asymptotics of this type is clearly required; this state of affairs is expressed both in recent mathematical and physical literature. For example, the editors of the collected volume [106] write in its preface: One can hope that in the near future a computational pro- cedure for fields with complex phase, similar to the usual one for fields with real phase, will be developed. Softcover reprint of the original 1st ed. 1994.
2
Symbolbild
The Complex WKB Method for Nonlinear Equations: Linear Theory: I
DE PB NW
ISBN: 9783034896696 bzw. 3034896697, in Deutsch, Springer Basel, Taschenbuch, neu.
Von Händler/Antiquariat, THE SAINT BOOKSTORE [51194787], Southport, United Kingdom.
BRAND NEW PRINT ON DEMAND., The Complex WKB Method for Nonlinear Equations: Linear Theory: I, Victor P. Maslov, A. B. Sossinsky, M.A. Shishkova, A. B. Sossinsky, This book deals with asymptotic solutions of linear and nonlinear equa- tions which decay as h ---+ 0 outside a neighborhood of certain points, curves and surfaces. Such solutions are almost everywhere well approximated by the functions cp(x) exp{iS(x)/h}, x E 1R3, where S(x) is complex, and ImS(x) ~ O. When the phase S(x) is real (ImS(x) = 0), the method for obtaining asymp- totics of this type is known in quantum mechanics as the WKB-method. We preserve this terminology in the case ImS(x) ~ 0 and develop the method for a wide class of problems in mathematical physics. Asymptotics of this type were constructed recently for many linear prob- lems of mathematical physics; certain specific formulas were obtained by differ- ent methods (V. M. Babich [5 -7], V. P. Lazutkin [76], A. A. Sokolov, 1. M. Ter- nov [113], J. Schwinger [107, 108], E. J. Heller [53], G. A. Hagedorn [50, 51], V. N. Bayer, V. M. Katkov [21], N. A. Chernikov [35] and others). However, a general (Hamiltonian) formalism for obtaining asymptotics of this type is clearly required; this state of affairs is expressed both in recent mathematical and physical literature. For example, the editors of the collected volume [106] write in its preface: "One can hope that in the near future a computational pro- cedure for fields with complex phase, similar to the usual one for fields with real phase, will be developed.
BRAND NEW PRINT ON DEMAND., The Complex WKB Method for Nonlinear Equations: Linear Theory: I, Victor P. Maslov, A. B. Sossinsky, M.A. Shishkova, A. B. Sossinsky, This book deals with asymptotic solutions of linear and nonlinear equa- tions which decay as h ---+ 0 outside a neighborhood of certain points, curves and surfaces. Such solutions are almost everywhere well approximated by the functions cp(x) exp{iS(x)/h}, x E 1R3, where S(x) is complex, and ImS(x) ~ O. When the phase S(x) is real (ImS(x) = 0), the method for obtaining asymp- totics of this type is known in quantum mechanics as the WKB-method. We preserve this terminology in the case ImS(x) ~ 0 and develop the method for a wide class of problems in mathematical physics. Asymptotics of this type were constructed recently for many linear prob- lems of mathematical physics; certain specific formulas were obtained by differ- ent methods (V. M. Babich [5 -7], V. P. Lazutkin [76], A. A. Sokolov, 1. M. Ter- nov [113], J. Schwinger [107, 108], E. J. Heller [53], G. A. Hagedorn [50, 51], V. N. Bayer, V. M. Katkov [21], N. A. Chernikov [35] and others). However, a general (Hamiltonian) formalism for obtaining asymptotics of this type is clearly required; this state of affairs is expressed both in recent mathematical and physical literature. For example, the editors of the collected volume [106] write in its preface: "One can hope that in the near future a computational pro- cedure for fields with complex phase, similar to the usual one for fields with real phase, will be developed.
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The Complex WKB Method for Nonlinear Equations I (2012)
DE PB NW
ISBN: 9783034896696 bzw. 3034896697, in Deutsch, Birkhauser Boston Inc, Taschenbuch, neu.
Lieferung aus: Schweiz, Versandfertig innert 6 - 9 Tagen.
Linear Theory, When this book was first published (in Russian), it proved to become the fountainhead of a major stream of important papers in mathematics, physics and even chemistry; indeed, it formed the basis of new methodology and opened new directions for research. The present English edition includes new examples of applications to physics, hitherto unpublished or available only in Russian. Its central mathematical idea is to use topological methods to analyze isotropic invariant manifolds in order to obtain asymptotic series of eigenvalues and eigenvectors for the multi-dimensional Schrödinger equation, and also to take into account the so-called tunnel effects. Finite-dimensional linear theory is reviewed in detail. Infinite-dimensional linear theory and its applications to quantum statistics and quantum field theory, as well as the nonlinear theory (involving instantons), will be considered in a second volume. Taschenbuch, 06.10.2012.
Linear Theory, When this book was first published (in Russian), it proved to become the fountainhead of a major stream of important papers in mathematics, physics and even chemistry; indeed, it formed the basis of new methodology and opened new directions for research. The present English edition includes new examples of applications to physics, hitherto unpublished or available only in Russian. Its central mathematical idea is to use topological methods to analyze isotropic invariant manifolds in order to obtain asymptotic series of eigenvalues and eigenvectors for the multi-dimensional Schrödinger equation, and also to take into account the so-called tunnel effects. Finite-dimensional linear theory is reviewed in detail. Infinite-dimensional linear theory and its applications to quantum statistics and quantum field theory, as well as the nonlinear theory (involving instantons), will be considered in a second volume. Taschenbuch, 06.10.2012.
4
The Complex WKB Method for Nonlinear Equations I: Linear Theory
EN PB US
ISBN: 9783034896696 bzw. 3034896697, in Englisch, Birkhauser Basel, Birkhauser Basel, Birkhauser Basel, Taschenbuch, gebraucht.
Lieferung aus: Vereinigte Staaten von Amerika, zzgl. Versandkosten, Free Shipping on eligible orders over $25, in-stock.
Victor P. Maslov, M.A. Shishkova (Translator), A.B. Sossinsky (Translator),Paperback - Softcover reprint of the original 1st ed. 1994,Series: Progress in Mathematical Physics Series 16, English-language edition, Pub by Birkhauser Basel.
Victor P. Maslov, M.A. Shishkova (Translator), A.B. Sossinsky (Translator),Paperback - Softcover reprint of the original 1st ed. 1994,Series: Progress in Mathematical Physics Series 16, English-language edition, Pub by Birkhauser Basel.
5
The Complex WKB Method for Nonlinear Equations I : Linear Theory
EN NW
ISBN: 9783034896696 bzw. 3034896697, in Englisch, neu.
Lieferung aus: Vereinigtes Königreich Großbritannien und Nordirland, zzgl. Versandkosten.
When this book was first published (in Russian), it proved to become the fountainhead of a major stream of important papers in mathematics, physics and even chemistry;...
When this book was first published (in Russian), it proved to become the fountainhead of a major stream of important papers in mathematics, physics and even chemistry;...
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