Nonlinear waves: theory, computer simulation, experiment
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 f…
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- Full title :Nonlinear waves : theory, computer simulation, experiment / M.D. Todorov.
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, 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.
Read More ↓Edition Statements
- Publication Date:2018
Publication Statements
- Publisher(s):Morgan & Claypool Publishers
- Place of Publication:San Rafael [California] (40 Oak Drive, San Rafael, CA, 94903, USA)
- Language:eng
- Publication Date:2018
Notes
"Version: 20180801"--Title page verso
Title from PDF title page (viewed on September 10, 2018).
The Physical Object
- Description:1 online resource (1 PDF (various pagings)) : : illustrations (some color)
Edition Identifiers
- ISBN:9781643270470, 1643270478, 9781643270456, 1643270451, 1643270443, 9781643270449
- DOI:10.1088/978-1-64327-047-0
- oclc:on1052762638
- LC Classification:QA927
- Dewey Decimal:530.155355
Table of 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 solito…
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