Ebook: Solitons in Molecular Systems
Author: A. S. Davydov (auth.)
- Tags: Theoretical Mathematical and Computational Physics, Partial Differential Equations, Mathematical Modeling and Industrial Mathematics
- Series: Mathematics and Its Applications 4
- Year: 1985
- Publisher: Springer Netherlands
- Edition: 1
- Language: English
- pdf
Approach your problems from the It isn't that they can't see the end and begin with the answers. solution. It is that they can't Then one day, perhaps you will see the problem. find the final question. G.K. Chesterton. The Scandal of 'The Hermit Clad in Crane Father Brown 'The Point of a Pin'. Feathers' in R. van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of mono graphs and textbooks on increasingly topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical pro gramming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electric engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "complete integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classifica tion schemes. The draw upon widely different sections of mathematics.
Content:
Front Matter....Pages i-xviii
Collective Excitations in Quasi-Periodical Molecular Structures....Pages 1-23
Excitations of Solitons in One-Dimensional Systems....Pages 24-36
Dynamical Properties of Solitons....Pages 37-43
Solitons in Molecular Systems with Nonlinear Intermolecular Interactions....Pages 44-60
Super-Sound Acoustic Solitons....Pages 61-70
Theory of Electron Transfer by Solitons....Pages 71-93
Space-Periodic Excitations in Nonlinear Systems....Pages 94-133
Long Waves in Nonlinear Media with Cubic Dispersion....Pages 134-163
The Nonlinear Sine-Gordon Equation....Pages 164-207
Some Nonlinear Phenomena in Solids....Pages 208-218
Conformal Excitations in One-Dimensional Molecular Systems....Pages 219-226
Solitons and Proton Motion in Molecular Systems with Hydrogen Bonds....Pages 227-241
Three-Dimensional Solitons (Polarons) in Ionic Crystals....Pages 242-259
Back Matter....Pages 260-319
Content:
Front Matter....Pages i-xviii
Collective Excitations in Quasi-Periodical Molecular Structures....Pages 1-23
Excitations of Solitons in One-Dimensional Systems....Pages 24-36
Dynamical Properties of Solitons....Pages 37-43
Solitons in Molecular Systems with Nonlinear Intermolecular Interactions....Pages 44-60
Super-Sound Acoustic Solitons....Pages 61-70
Theory of Electron Transfer by Solitons....Pages 71-93
Space-Periodic Excitations in Nonlinear Systems....Pages 94-133
Long Waves in Nonlinear Media with Cubic Dispersion....Pages 134-163
The Nonlinear Sine-Gordon Equation....Pages 164-207
Some Nonlinear Phenomena in Solids....Pages 208-218
Conformal Excitations in One-Dimensional Molecular Systems....Pages 219-226
Solitons and Proton Motion in Molecular Systems with Hydrogen Bonds....Pages 227-241
Three-Dimensional Solitons (Polarons) in Ionic Crystals....Pages 242-259
Back Matter....Pages 260-319
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