M.D. Todorov Nonlinear Waves: Theory, Computer Simulation, Experiment 9781643270449

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Автор: M.D. Todorov
Название: Nonlinear Waves: Theory, Computer Simulation, Experiment
ISBN: 9781643270449
Издательство: Mare Nostrum (Eurospan)
Классификация:

Классическая механика

Динамика и статика

Математическая физика

ISBN-10: 1643270443
Обложка/Формат: Paperback
Страницы: 184
Вес: 0.33 кг.
Дата издания: 30.09.2018
Серия: Physics
Язык: English
Размер: 254 x 178 x 10
Ключевые слова: Classical mechanics,Dynamics & statics,Mathematical physics, SCIENCE / Mechanics / General,SCIENCE / Mechanics / Dynamics,SCIENCE / Physics / Mathematical & Computational
Подзаголовок: Theory, computer simulation, experiment
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Поставляется из: Англии
Описание: 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.The system of coupled nonlinear Schroedinger equations known as well as the vector Schroedinger equation is a soliton supporting dynamical system. It is considered as a model of light propagation in Kerr isotropic media. Along with that, the phenomenology of the equation opens a prospect of investigating the quasi-particle behavior of the interacting solitons. The initial polarization of the vector Schroedinger equation and its evolution evolves from the vector nature of the model. The existence of exact (analytical) solutions usually is rendered to simpler models, while for the vector Schroedinger equation such solutions are not known. This determines the role of the numerical schemes and approaches. The vector Schroedinger equation is a spring-board for combining the reduced integrability and conservation laws in a discrete level.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 reliable algorithms for treating the governing equations. Along with the nonintegrability, one more problem appears here - the multidimensionality and necessity to split and linearize the operators in the appropriate way.

Nonlinear Waves: Theory, Computer Simulation, Experiment, M.D. Todorov