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Nonlinear waves : theory, computer simulation, experiment

Author: Michail D Todorov; Morgan & Claypool Publishers,; Institute of Physics (Great Britain),
Publisher: San Rafael [California] (40 Oak Drive, San Rafael, CA, 94903, USA) : Morgan & Claypool Publishers, Bristol [England] (Temple Circus, Temple Way, Bristol BS1 6HG, UK) : IOP Publishing, [2018] [2018]
Series: IOP (Series)., Release 5.; IOP concise physics.; Series on wave phenomena in the physical sciences.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
The Boussinesq equation is the first model of surface waves in shallow water that considers the nonlinearity and the dispersion and their interaction as a reason for wave stability known as the Boussinesq paradigm. This balance bears solitary waves that behave like quasi-particles. At present, there are some Boussinesq-like equations. The prevalent part of the known analytical and numerical solutions, however,  Read more...
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Details

Additional Physical Format: Print version:
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Michail D Todorov; Morgan & Claypool Publishers,; Institute of Physics (Great Britain),
ISBN: 9781643270470 1643270478 9781643270456 1643270451 1643270443 9781643270449
OCLC Number: 1052762638
Notes: "Version: 20180801"--Title page verso.
"A Morgan & Claypool publication as part of IOP Concise Physics"--Title page verso.
Description: 1 PDF (various pagings) : illustrations (some color).
Details: Mode of access: World Wide Web.; System requirements: Adobe Acrobat Reader, EPUB reader, or Kindle reader.
Contents: 1. Two-dimensional Boussinesq equation. Boussinesq paradigm and soliton solutions --
1.1. Boussinesq equations. Generalized wave equation --
1.2. Investigation of the long-time evolution of localized solutions of a dispersive wave system --
1.3. Numerical implementation of Fourier-transform method for generalized wave equations --
1.4. Perturbation solution for the 2D shallow-water waves --
1.5. Boussinesq paradigm equation and the experimental measurement --
1.6. Development and realization of efficient numerical methods, algorithms and scientific software for 2D nonsteady Boussinesq paradigm equation. Comparative analysis of the results 2. Systems of coupled nonlinear Schrödinger equations. Vector Schrödinger equation --
2.1. Conservative scheme in complex arithmetic for vector nonlinear Schrödinger equations --
2.2. Finite-difference implementation of conserved properties of the vector nonlinear Schrödinger equation (VNLSE) --
2.3. Collision dynamics of circularly polarized solitons in nonintegrable VNLSE --
2.4. Impact of the large cross-modulation parameter on the collision dynamics of quasi-particles governed by vector nonlinear Schrödinger equation --
2.5. Repelling soliton collisions in vector nonlinear Schrödinger equation with negative cross modulation --
2.6. On the solution of the system of ordinary differential equations governing the polarized stationary solutions of vector nonlinear Schrödinger equation --
2.7. Collision dynamics of elliptically polarized solitons in vector nonlinear Schrödinger equation --
2.8. Collision dynamics of polarized solitons in linearly coupled vector nonlinear Schrödinger equation --
2.9. Polarization dynamics during takeover collisions of solitons in vector nonlinear Schrödinger equation --
2.10. The effect of the elliptic polarization on the quasi-particle dynamics of linearly coupled vector nonlinear Schrödinger equation --
2.11. Vector nonlinear Schrödinger equation with different cross-modulation rates --
2.12. Asymptotic behavior of Manakov solitons --
2.13. Manakov solitons and effects of external potential wells and humps 2-105 3. Ultrashort optical pulses. Envelope dispersive equations --
3.1. On a method for solving of multidimensional equations of mathematical physics --
3.2. Dynamics of high-intensity ultrashort light pulses at some basic propagation regimes --
3.3. (3+1)D nonlinear Schrödinger equation --
3.4. (3+1)D nonlinear envelope equation (NEE) --
3.5. Summary of the studies.
Series Title: IOP (Series)., Release 5.; IOP concise physics.; Series on wave phenomena in the physical sciences.
Responsibility: M.D. Todorov.

Abstract:

The experimental observation and measurement of ultrashort pulses in waveguides is a hard job and this is the reason and stimulus to create mathematical models for computer simulations, as well as  Read more...

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