Nonlinear waves :theory, computer simulation, experiment /

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"Version: 20180801"--Title page verso."A Morgan & Claypool publication as part of IOP Concise Physics"--Title page verso.Includes bibliographical references.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 results2. Systems of coupled nonlinear Schr?odinger equations. Vector Schr?odinger equation -- 2.1. Conservative scheme in complex arithmetic for vector nonlinear Schr?odinger equations -- 2.2. Finite-difference implementation of conserved properties of the vector nonlinear Schr?odinger 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 Schr?odinger equation -- 2.5. Repelling soliton collisions in vector nonlinear Schr?odinger 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 Schr?odinger equation -- 2.7. Collision dynamics of elliptically polarized solitons in vector nonlinear Schr?odinger equation -- 2.8. Collision dynamics of polarized solitons in linearly coupled vector nonlinear Schr?odinger equation -- 2.9. Polarization dynamics during takeover collisions of solitons in vector nonlinear Schr?odinger equation -- 2.10. The effect of the elliptic polarization on the quasi-particle dynamics of linearly coupled vector nonlinear Schr?odinger equation -- 2.11. Vector nonlinear Schr?odinger 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 2-1053. 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 Schr?odinger equation -- 3.4. (3+1)D nonlinear envelope equation (NEE) -- 3.5. Summary of the studies.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.Also available in print.Mode of access: World Wide Web.System requirements: Adobe Acrobat Reader, EPUB reader, or Kindle reader.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.Title from PDF title page (viewed on September 10, 2018).

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: .,

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1 online resource (various pagings) :illustrations (some color).

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English

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9781643270470

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530.155355

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Mathematical physics.
Nonlinear wave equations.
SCIENCE / Mechanics / Dynamics.
Dynamics & statistics.

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M.D. Todorov.

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