Semiclassical Soliton Ensembles For The Focusing Nonlinear Schrodinger Equation Am 154 PDF Download
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Author | : Spyridon Kamvissis |
Publisher | : Princeton University Press |
Total Pages | : 281 |
Release | : 2003-09-07 |
Genre | : Mathematics |
ISBN | : 069111482X |
Download Semiclassical Soliton Ensembles for the Focusing Nonlinear Schrodinger Equation (AM-154) Book in PDF, ePub and Kindle
Providing an asymptotic analysis via completely integrable techniques, of the initial value problem for the focusing nonlinear Schrodinger equation in the semiclassical asymptotic regime, this text exploits complete integrability to establish pointwise asymptotics for this problem's solution.
Author | : Spyridon Kamvissis |
Publisher | : |
Total Pages | : 367 |
Release | : 2002 |
Genre | : |
ISBN | : |
Download Semiclassical Soliton Ensembles for the Focusing Nonlinear Schrödinger Equation Book in PDF, ePub and Kindle
Author | : J. Baik |
Publisher | : Princeton University Press |
Total Pages | : 179 |
Release | : 2007-01-02 |
Genre | : Mathematics |
ISBN | : 1400837138 |
Download Discrete Orthogonal Polynomials. (AM-164) Book in PDF, ePub and Kindle
This book describes the theory and applications of discrete orthogonal polynomials--polynomials that are orthogonal on a finite set. Unlike other books, Discrete Orthogonal Polynomials addresses completely general weight functions and presents a new methodology for handling the discrete weights case. J. Baik, T. Kriecherbauer, K. T.-R. McLaughlin & P. D. Miller focus on asymptotic aspects of general, nonclassical discrete orthogonal polynomials and set out applications of current interest. Topics covered include the probability theory of discrete orthogonal polynomial ensembles and the continuum limit of the Toda lattice. The primary concern throughout is the asymptotic behavior of discrete orthogonal polynomials for general, nonclassical measures, in the joint limit where the degree increases as some fraction of the total number of points of collocation. The book formulates the orthogonality conditions defining these polynomials as a kind of Riemann-Hilbert problem and then generalizes the steepest descent method for such a problem to carry out the necessary asymptotic analysis.
Author | : Miguel Onorato |
Publisher | : Springer |
Total Pages | : 376 |
Release | : 2016-09-19 |
Genre | : Science |
ISBN | : 331939214X |
Download Rogue and Shock Waves in Nonlinear Dispersive Media Book in PDF, ePub and Kindle
This self-contained set of lectures addresses a gap in the literature by providing a systematic link between the theoretical foundations of the subject matter and cutting-edge applications in both geophysical fluid dynamics and nonlinear optics. Rogue and shock waves are phenomena that may occur in the propagation of waves in any nonlinear dispersive medium. Accordingly, they have been observed in disparate settings – as ocean waves, in nonlinear optics, in Bose-Einstein condensates, and in plasmas. Rogue and dispersive shock waves are both characterized by the development of extremes: for the former, the wave amplitude becomes unusually large, while for the latter, gradients reach extreme values. Both aspects strongly influence the statistical properties of the wave propagation and are thus considered together here in terms of their underlying theoretical treatment. This book offers a self-contained graduate-level text intended as both an introduction and reference guide for a new generation of scientists working on rogue and shock wave phenomena across a broad range of fields in applied physics and geophysics.
Author | : Remi Carles |
Publisher | : World Scientific |
Total Pages | : 256 |
Release | : 2008-03-04 |
Genre | : Mathematics |
ISBN | : 9814471747 |
Download Semi-classical Analysis For Nonlinear Schrodinger Equations Book in PDF, ePub and Kindle
These lecture notes review recent results on the high-frequency analysis of nonlinear Schrödinger equations in the presence of an external potential. The book consists of two relatively independent parts: WKB analysis, and caustic crossing. In the first part, the basic linear WKB theory is constructed and then extended to the nonlinear framework. The most difficult supercritical case is discussed in detail, together with some of its consequences concerning instability phenomena. Applications of WKB analysis to functional analysis, in particular to the Cauchy problem for nonlinear Schrödinger equations, are also given. In the second part, caustic crossing is described, especially when the caustic is reduced to a point, and the link with nonlinear scattering operators is investigated.These notes are self-contained and combine selected articles written by the author over the past ten years in a coherent manner, with some simplified proofs. Examples and figures are provided to support the intuition, and comparisons with other equations such as the nonlinear wave equation are provided.
Author | : Rémi Carles |
Publisher | : World Scientific Publishing Company Incorporated |
Total Pages | : 243 |
Release | : 2008 |
Genre | : Mathematics |
ISBN | : 9812793127 |
Download Semi-classical Analysis for Nonlinear Schrödinger Equations Book in PDF, ePub and Kindle
Author | : |
Publisher | : |
Total Pages | : 1574 |
Release | : 2004 |
Genre | : Mathematics |
ISBN | : |
Download Mathematical Reviews Book in PDF, ePub and Kindle
Author | : Mark Green |
Publisher | : Princeton University Press |
Total Pages | : 298 |
Release | : 2012-04-22 |
Genre | : Mathematics |
ISBN | : 1400842735 |
Download Mumford-Tate Groups and Domains Book in PDF, ePub and Kindle
Mumford-Tate groups are the fundamental symmetry groups of Hodge theory, a subject which rests at the center of contemporary complex algebraic geometry. This book is the first comprehensive exploration of Mumford-Tate groups and domains. Containing basic theory and a wealth of new views and results, it will become an essential resource for graduate students and researchers. Although Mumford-Tate groups can be defined for general structures, their theory and use to date has mainly been in the classical case of abelian varieties. While the book does examine this area, it focuses on the nonclassical case. The general theory turns out to be very rich, such as in the unexpected connections of finite dimensional and infinite dimensional representation theory of real, semisimple Lie groups. The authors give the complete classification of Hodge representations, a topic that should become a standard in the finite-dimensional representation theory of noncompact, real, semisimple Lie groups. They also indicate that in the future, a connection seems ready to be made between Lie groups that admit discrete series representations and the study of automorphic cohomology on quotients of Mumford-Tate domains by arithmetic groups. Bringing together complex geometry, representation theory, and arithmetic, this book opens up a fresh perspective on an important subject.
Author | : L. Boutet de Monvel |
Publisher | : Princeton University Press |
Total Pages | : 166 |
Release | : 2016-03-02 |
Genre | : Mathematics |
ISBN | : 1400881447 |
Download The Spectral Theory of Toeplitz Operators. (AM-99), Volume 99 Book in PDF, ePub and Kindle
The theory of Toeplitz operators has come to resemble more and more in recent years the classical theory of pseudodifferential operators. For instance, Toeplitz operators possess a symbolic calculus analogous to the usual symbolic calculus, and by symbolic means one can construct parametrices for Toeplitz operators and create new Toeplitz operators out of old ones by functional operations. If P is a self-adjoint pseudodifferential operator on a compact manifold with an elliptic symbol that is of order greater than zero, then it has a discrete spectrum. Also, it is well known that the asymptotic behavior of its eigenvalues is closely related to the behavior of the bicharacteristic flow generated by its symbol. It is natural to ask if similar results are true for Toeplitz operators. In the course of answering this question, the authors explore in depth the analogies between Toeplitz operators and pseudodifferential operators and show that both can be viewed as the "quantized" objects associated with functions on compact contact manifolds.
Author | : Spyros Alexakis |
Publisher | : Princeton University Press |
Total Pages | : 568 |
Release | : 2012-05-06 |
Genre | : Mathematics |
ISBN | : 1400842727 |
Download The Decomposition of Global Conformal Invariants (AM-182) Book in PDF, ePub and Kindle
This book addresses a basic question in differential geometry that was first considered by physicists Stanley Deser and Adam Schwimmer in 1993 in their study of conformal anomalies. The question concerns conformally invariant functionals on the space of Riemannian metrics over a given manifold. These functionals act on a metric by first constructing a Riemannian scalar out of it, and then integrating this scalar over the manifold. Suppose this integral remains invariant under conformal re-scalings of the underlying metric. What information can one then deduce about the Riemannian scalar? Deser and Schwimmer asserted that the Riemannian scalar must be a linear combination of three obvious candidates, each of which clearly satisfies the required property: a local conformal invariant, a divergence of a Riemannian vector field, and the Chern-Gauss-Bonnet integrand. This book provides a proof of this conjecture. The result itself sheds light on the algebraic structure of conformal anomalies, which appear in many settings in theoretical physics. It also clarifies the geometric significance of the renormalized volume of asymptotically hyperbolic Einstein manifolds. The methods introduced here make an interesting connection between algebraic properties of local invariants--such as the classical Riemannian invariants and the more recently studied conformal invariants--and the study of global invariants, in this case conformally invariant integrals. Key tools used to establish this connection include the Fefferman-Graham ambient metric and the author's super divergence formula.