Introduction to the mathematical physics of nonlinear waves / Minoru Fujimoto.

Format:

Book

Author/Creator:

Fujimoto, Minoru, author.

Contributor:

Institute of Physics (Great Britain), publisher.

Series:

IOP ebooks. 2021 collection.

IOP ebooks. [2021 collection]

Language:

English

Subjects (All):

Nonlinear waves.

Nonlinear theories.

Nonlinear wave equations.

Mathematical physics.

Physical Description:

1 online resource (various pagings) : illustrations.

Edition:

Second edition.

Place of Publication:

Bristol [England] (Temple Circus, Temple Way, Bristol BS1 6HG, UK) : IOP Publishing, [2021]

System Details:

Mode of access: World Wide Web.

System requirements: Adobe Acrobat Reader, EPUB reader, or Kindle reader.

Biography/History:

Minoru Fujimoto is a retired professor from the University of Guelph, Canada, where he conducted research in the field of magnetic resonance studies on structural phase transitions in crystals which has currently been extended to theoretical work with soliton dynamics especially as applied to crystalline condensed matter systems. He is the author of numerous papers and several books including Physics of Classical Electromagnetism and Thermodynamics of Crystalline States (Springer); Introduction to Mathematical Physics of Nonlinear Waves and Solitons in Crystalline Processes (IOP Publishing). He lives in Mississauga, Ontario.

Summary:

Written for students at upper-undergraduate and graduate levels, it is suitable for advanced physics courses on nonlinear physics. The book covers the fundamental properties of nonlinear waves, dealing with both theory and experiment. The aim is to emphasize established tools and introduce new methods underpinning important new developments in this field, especially as applied to solid-state materials. The updated edition has been extended to emphasize the importance of thermodynamics in a description of modulated crystals and contains new chapters on superconductivity that can be interpreted by the soliton mechanism. It is also updated to include new end-of-chapter problems.

Contents:

1. Nonlinearity and elliptic functions in classical mechanics

1.1. A pendulum

1.2. Vibration by a nonlinear spring force

1.3. Hyperbolic and elliptic functions

1.4. A jumping rope

1.5. Variation principle

1.6. Buckling of an elastic rod

2. Wave propagation, singularities, and boundary conditions

2.1. Elastic waves along a linear string in infinite length

2.2. Microwave transmission

2.3. Wave equations

2.4. Sound propagation in air

2.5. Asymptotic approximation in air space

3. Order variables for structural phase transitions

3.1. Symmetry group in crystals

3.2. Solitons and the Ising model for pseudospin correlations

3.3. Macroscopic views of structural phase transitions

3.4. Observing critical anomalies

4. Soft modes of lattice displacements

4.1. The Lyddane-Sachs-Teller relation

4.2. Soft modes in perovskite oxides

4.3. Dynamics of soft modes

4.4. Soft-mode frequency in modulated crystals

4.5. Optical studies on symmetry changes at critical temperature

5. Nonlinearity development in crystals : Korteweg-deVries' equation for collective order variables and the complex potential

5.1. The Korteweg-deVries equation

5.2. Thermal solution for the Weiss potential

5.3. Condensate pinning by the Weiss potential

5.4. Nonlinear waves and complex lattice potentials

5.5. The complex lattice potential

5.6. Isothermal phase transition and entropy production

6. Soliton mobility in time-temperature conversion for thermal processes : Riccati's theorem

6.1. Bargmann's theorem

6.2. Riccati's theorem and the modified Korteweg-deVries equation

6.3. Soliton mobility studied by computational analysis

7. Toda's lattice of correlation potentials

7.1. The Toda soliton lattice

7.2. Developing nonlinearity

7.3. Conversion to Korteweg-deVries' lattice potential

8. Scattering theory of the soliton lattice

8.1. Elemental waves

8.2. Scattering theory : dissipation, reflection, and transmission

8.3. Method of inverse scattering

8.4. Entropy production from soliton potentials

9. Pseudopotentials and sine-Gordon equation : topological correlations in domain structure

9.1. Pseudopotentials in mesoscopic phases

9.2. The sine-Gordon equation

9.3. Phase solitons in adiabatic processes

9.4. The Bäcklund transformation and domain boundaries

9.5. Computational studies of the Bäcklund transformation

10. Trigonal structural transitions : domain stability in topological order

10.1. The sine-Gordon equation

10.2. Observing adiabatic fluctuations

10.3. Toda's theory of domain stability

10.4. Kac's theory of nonlinearity for domain disorder

10.5. Domain separation and thermal and quasi-adiabatic transitions

10.6. Mesoscopic domains in topological disorder

11. Soliton theory of superconducting transitions

11.1. The Meissner effect and Fröhlich's proposal

11.2. Magnetic images of Fröhlich's interaction

11.3. The Cooper pair and persistent current

11.4. Critical temperatures and energy gap in superconducting transitions

11.5. Anderson's theory of superconducting phase transitions

11.6. Cuprate-layer structure and the Cooper pair

11.7. Meissner's effect in cuprate-layers and metallic hydrogen sulfide H3S

12. Irreducible thermodynamics of superconducting phase transitions

12.1. Superconducting phase transition

12.2. Electromagnetic properties of superconductors

12.3. The Ginzburg-Landau equation for superconducting phase transitions

12.4. Field theory of superconducting transitions.

Notes:

"IOP ebooks."

Includes bibliographical references.

Description based on online resource; title from digital title page (viewed on August 21, 2022)

Other Format:

Print version:

ISBN:

0-7503-3758-3

0-7503-3759-1

9780750337595

OCLC:

1275356606