Nonlinear waves [electronic resource] : theory, computer simulation, experiment / M.D. Todorov.

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...

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Bibliographic Details
Uniform Title:IOP (Series). Release 5.
IOP concise physics.
Series on wave phenomena in the physical sciences.
Main Author: Todorov, Michail D. (Author)
Corporate Authors: Morgan & Claypool Publishers (Publisher)
Institute of Physics (Great Britain) (Publisher)
Language:English
Published: San Rafael [California] (40 Oak Drive, San Rafael, CA, 94903, USA) : Morgan & Claypool Publishers, [2018]
Series:IOP (Series). Release 5.
IOP concise physics.
Series on wave phenomena in the physical sciences.
Subjects:
Nonlinear wave equations.
Mathematical physics.
Online Access:
IOP Concise Physics - Release 5: 2018 (IOPscience @ Institute of Physics)
Variant Title:
Nonlinear Waves: Theory, computer simulation, experiment
Format: Electronic eBook

MARC

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100 1 |a Todorov, Michail D.,  |e author. 
245 1 0 |a Nonlinear waves  |h [electronic resource] :  |b theory, computer simulation, experiment /  |c M.D. Todorov. 
246 2 |a Nonlinear Waves: Theory, computer simulation, experiment 
264 1 |a San Rafael [California] (40 Oak Drive, San Rafael, CA, 94903, USA) :  |b Morgan & Claypool Publishers,  |c [2018] 
264 2 |a Bristol [England] (Temple Circus, Temple Way, Bristol BS1 6HG, UK) :  |b IOP Publishing,  |c [2018] 
490 1 |a [IOP release 5] 
490 1 |a IOP concise physics,  |x 2053-2571 
490 1 |a Series on wave phenomena in the physical sciences 
500 |a "Version: 20180801"--Title page verso. 
500 |a "A Morgan & Claypool publication as part of IOP Concise Physics"--Title page verso. 
504 |a Includes bibliographical references. 
505 0 |a 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 
505 8 |a 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 
505 8 |a 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. 
520 3 |a 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, relates to the 1d case while for multidimensional cases, almost nothing is known so far. An exclusion is the solutions of the Kadomtsev-Petviashvili equation. The difficulties originate from the lack of known analytic initial conditions and the nonintegrability in the multidimensional case. Another problem is which kind of nonlinearity will keep the temporal stability of localized solutions. 
538 |a Mode of access: World Wide Web. 
538 |a System requirements: Adobe Acrobat Reader, EPUB reader, or Kindle reader. 
545 |a Michail Todorov graduated in 1984 and received PhD degree in 1989 from the St. Kliment Ohridski University of Sofia, Bulgaria. Since 1990, he has been Associate Professor and Full Professor (2012) with the Department of Applied Mathematics and Computer Science by the Technical University of Sofia, Bulgaria. For the last few years, his primary research areas have been mathematical modeling, computational studies, and scientific computing of nonlinear phenomena including soliton interactions, nonlinear electrodynamics, nonlinear optics, mathematical biology and bioengineering, and astrophysics. 
650 0 |a Nonlinear wave equations. 
650 0 |a Mathematical physics. 
710 2 |a Morgan & Claypool Publishers,  |e publisher. 
710 2 |a Institute of Physics (Great Britain),  |e publisher. 
773 0 |t IOP Concise Physics - Release 5   |d IOP Publishing Limited 
776 0 8 |i Print version:  |z 9781643270449 
830 0 |a IOP (Series).  |p Release 5. 
830 0 |a IOP concise physics. 
830 0 |a Series on wave phenomena in the physical sciences. 
856 4 0 |y Access Content Online(from IOP Concise Physics - Release 5)  |u https://ezproxy.msu.edu/login?url=https://iopscience.iop.org/book/mono/978-1-64327-047-0  |z IOP Concise Physics - Release 5: 2018