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Author: Clément Gallo
Publisher:
ISBN:
Category :
Languages : en
Pages : 211
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Book Description
This PhD thesis is concerned with non-zero at infinity solutions of some nonlinear dispersive equations. We establish existence results for dark solitons of nonlinear Schrödinger equations and of system of two coupled nonlinear Schrödinger equations, in dimension 1. We study the linear stability of a special kind of dark solitons of nonlinear Schrödinger equations: the black solitons. We study the Cauchy problem for the linear and for the nonlinear Schrödinger equations on the Zhidkov spaces X^k(R^n). We also consider the same initial value problem on the affine space phi+H^1, where phi is a (non -zero at infinity) regular function with finite energy. We finally study the Cauchy problem for nonlinear dispersive equations which look like the Koiteweg-de Vries or the Benjamin-Ono equations, on the Zhidkov spaces X^s(R).
Author: Clément Gallo
Publisher:
ISBN:
Category :
Languages : en
Pages : 211
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Book Description
This PhD thesis is concerned with non-zero at infinity solutions of some nonlinear dispersive equations. We establish existence results for dark solitons of nonlinear Schrödinger equations and of system of two coupled nonlinear Schrödinger equations, in dimension 1. We study the linear stability of a special kind of dark solitons of nonlinear Schrödinger equations: the black solitons. We study the Cauchy problem for the linear and for the nonlinear Schrödinger equations on the Zhidkov spaces X^k(R^n). We also consider the same initial value problem on the affine space phi+H^1, where phi is a (non -zero at infinity) regular function with finite energy. We finally study the Cauchy problem for nonlinear dispersive equations which look like the Koiteweg-de Vries or the Benjamin-Ono equations, on the Zhidkov spaces X^s(R).
Author:
Publisher:
ISBN:
Category : Electronic journals
Languages : en
Pages : 1080
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Book Description
Author: W.-M. Ni
Publisher: Springer Science & Business Media
ISBN: 1461396085
Category : Mathematics
Languages : en
Pages : 364
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Book Description
In recent years considerable interest has been focused on nonlinear diffu sion problems, the archetypical equation for these being Ut = ~U + f(u). Here ~ denotes the n-dimensional Laplacian, the solution u = u(x, t) is defined over some space-time domain of the form n x [O,T], and f(u) is a given real function whose form is determined by various physical and mathematical applications. These applications have become more varied and widespread as problem after problem has been shown to lead to an equation of this type or to its time-independent counterpart, the elliptic equation of equilibrium ~u+f(u)=O. Particular cases arise, for example, in population genetics, the physics of nu clear stability, phase transitions between liquids and gases, flows in porous media, the Lend-Emden equation of astrophysics, various simplified com bustion models, and in determining metrics which realize given scalar or Gaussian curvatures. In the latter direction, for example, the problem of finding conformal metrics with prescribed curvature leads to a ground state problem involving critical exponents. Thus not only analysts, but geome ters as well, can find common ground in the present work. The corresponding mathematical problem is to determine how the struc ture of the nonlinear function f(u) influences the behavior of the solution.
Author: James Johnston Stoker
Publisher: Courier Dover Publications
ISBN: 0486839923
Category : Science
Languages : en
Pages : 593
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Book Description
First published in 1957, this is a classic monograph in the area of applied mathematics. It offers a connected account of the mathematical theory of wave motion in a liquid with a free surface and subjected to gravitational and other forces, together with applications to a wide variety of concrete physical problems. A never-surpassed text, it remains of permanent value to a wide range of scientists and engineers concerned with problems in fluid mechanics. The four-part treatment begins with a presentation of the derivation of the basic hydrodynamic theory for non-viscous incompressible fluids and a description of the two principal approximate theories that form the basis for the rest of the book. The second section centers on the approximate theory that results from small-amplitude wave motions. A consideration of problems involving waves in shallow water follows, and the text concludes with a selection of problems solved in terms of the exact theory. Despite the diversity of its topics, this text offers a unified, readable, and largely self-contained treatment.
Author: David Looseley
Publisher: Oxford University Press
ISBN: 1781382573
Category : Biography & Autobiography
Languages : en
Pages : 264
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Book Description
The world-famous French singer Édith Piaf (1915-63) was never just a singer. This book suggests new ways of understanding her, her myth and her meanings over time at home and abroad, by proposing the notion of an 'imagined Piaf.
Author: Thierry Dauxois
Publisher: Cambridge University Press
ISBN: 0521854210
Category : Mathematics
Languages : en
Pages : 435
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Book Description
This textbook gives an instructive view of solitons and their applications for advanced students of physics.
Author: Olivier Darrigol
Publisher: Oxford University Press
ISBN: 0198568436
Category : Mathematics
Languages : en
Pages : 372
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Book Description
This book provides the first fully-fledged history of hydrodynamics, including lively accounts of the concrete problems of hydraulics, navigation, blood circulation, meteorology, and aeronautics that motivated the main conceptual innovations. Richly illustrated, technically competent, and philosophically sensitive, it should attract a broad audience and become a standard reference for any one interested in fluid mechanics.
Author: M. Burak Erdoğan
Publisher: Cambridge University Press
ISBN: 1107149045
Category : Mathematics
Languages : en
Pages : 203
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Book Description
Introduces nonlinear dispersive partial differential equations in a detailed yet elementary way without compromising the depth and richness of the subject.
Author: M D Todorov
Publisher: Morgan & Claypool Publishers
ISBN: 1643270478
Category : Science
Languages : en
Pages : 185
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Book Description
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.
Author: Daniele Faccio
Publisher: Springer
ISBN: 331900266X
Category : Science
Languages : en
Pages : 452
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Book Description
Analogue Gravity Phenomenology is a collection of contributions that cover a vast range of areas in physics, ranging from surface wave propagation in fluids to nonlinear optics. The underlying common aspect of all these topics, and hence the main focus and perspective from which they are explained here, is the attempt to develop analogue models for gravitational systems. The original and main motivation of the field is the verification and study of Hawking radiation from a horizon: the enabling feature is the possibility to generate horizons in the laboratory with a wide range of physical systems that involve a flow of one kind or another. The years around 2010 and onwards witnessed a sudden surge of experimental activity in this expanding field of research. However, building an expertise in analogue gravity requires the researcher to be equipped with a rather broad range of knowledge and interests. The aim of this book is to bring the reader up to date with the latest developments and provide the basic background required in order to appreciate the goals, difficulties, and success stories in the field of analogue gravity. Each chapter of the book treats a different topic explained in detail by the major experts for each specific discipline. The first chapters give an overview of black hole spacetimes and Hawking radiation before moving on to describe the large variety of analogue spacetimes that have been proposed and are currently under investigation. This introductory part is then followed by an in-depth description of what are currently the three most promising analogue spacetime settings, namely surface waves in flowing fluids, acoustic oscillations in Bose-Einstein condensates and electromagnetic waves in nonlinear optics. Both theory and experimental endeavours are explained in detail. The final chapters refer to other aspects of analogue gravity beyond the study of Hawking radiation, such as Lorentz invariance violations and Brownian motion in curved spacetimes, before concluding with a return to the origins of the field and a description of the available observational evidence for horizons in astrophysical black holes.
