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| Author | : Naruyoshi Asano |
| Publisher | : Longman Scientific and Technical |
| Total Pages | : 448 |
| Release | : 1990 |
| Genre | : Mathematics |
| ISBN | : |
| Author | : Jianming He |
| Publisher | : |
| Total Pages | : 442 |
| Release | : 1997 |
| Genre | : Nonlinear wave equations |
| ISBN | : |
| Author | : Naruyoshi Asano |
| Publisher | : Longman |
| Total Pages | : 448 |
| Release | : 1990 |
| Genre | : Differential equations, Nonlinear |
| ISBN | : |
| Author | : Satyanad Kichenassamy |
| Publisher | : CRC Press |
| Total Pages | : 297 |
| Release | : 2021-05-30 |
| Genre | : Mathematics |
| ISBN | : 1000444724 |
This work examines the mathematical aspects of nonlinear wave propagation, emphasizing nonlinear hyperbolic problems. It introduces the tools that are most effective for exploring the problems of local and global existence, singularity formation, and large-time behaviour of solutions, and for the study of perturbation methods.
| Author | : Beatrice Pelloni |
| Publisher | : |
| Total Pages | : 560 |
| Release | : 1996 |
| Genre | : Nonlinear waves |
| ISBN | : |
| Author | : I D Iliev |
| Publisher | : CRC Press |
| Total Pages | : 412 |
| Release | : 1994-11-21 |
| Genre | : Mathematics |
| ISBN | : 9780582239630 |
Soliton theory as a method for solving some classes of nonlinear evolution equations (soliton equations) is one of the most actively developing topics in mathematical physics. This book presents some spectral theory methods for the investigation of soliton equations ad the inverse scattering problems related to these equations. The authors give the theory of expansions for the Sturm-Liouville operator and the Dirac operator. On this basis, the spectral theory of recursion operators generating Korteweg-de Vries type equations is presented and the Ablowitz-Kaup-Newell-Segur scheme, through which the inverse scattering method could be understood as a Fourier-type transformation, is considered. Following these ideas, the authors investigate some of the questions related to inverse spectral problems, i.e. uniqueness theorems, construction of explicit solutions and approximative methods for solving inverse scattering problems. A rigorous investigation of the stability of soliton solutions including solitary waves for equations which do not allow integration within inverse scattering method is also presented.
| Author | : Dominic P. Clemence |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 226 |
| Release | : 2005 |
| Genre | : Mathematics |
| ISBN | : 0821833499 |
Lively discussions and stimulating research were part of a five-day conference on Mathematical Methods in Nonlinear Wave Propagation sponsored by the NSF and CBMS. This volume is a collection of lectures and papers stemming from that event. Leading experts present dynamical systems and chaos, scattering and spectral theory, nonlinear wave equations, optimal control, optical waveguide design, and numerical simulation. The book is suitable for a diverse audience of mathematical specialists interested in fiber optic communications and other nonlinear phenomena. It is also suitable for engineers and other scientists interested in the mathematics of nonlinear wave propagation.
| Author | : Angela Slavova |
| Publisher | : World Scientific Publishing |
| Total Pages | : 208 |
| Release | : 2018-11-16 |
| Genre | : Mathematics |
| ISBN | : 9813271620 |
This volume provides an in-depth treatment of several equations and systems of mathematical physics, describing the propagation and interaction of nonlinear waves as different modifications of these: the KdV equation, Fornberg-Whitham equation, Vakhnenko equation, Camassa-Holm equation, several versions of the NLS equation, Kaup-Kupershmidt equation, Boussinesq paradigm, and Manakov system, amongst others, as well as symmetrizable quasilinear hyperbolic systems arising in fluid dynamics.Readers not familiar with the complicated methods used in the theory of the equations of mathematical physics (functional analysis, harmonic analysis, spectral theory, topological methods, a priori estimates, conservation laws) can easily be acquainted here with different solutions of some nonlinear PDEs written in a sharp form (waves), with their geometrical visualization and their interpretation. In many cases, explicit solutions (waves) having specific physical interpretation (solitons, kinks, peakons, ovals, loops, rogue waves) are found and their interactions are studied and geometrically visualized. To do this, classical methods coming from the theory of ordinary differential equations, the dressing method, Hirota's direct method and the method of the simplest equation are introduced and applied. At the end, the paradifferential approach is used.This volume is self-contained and equipped with simple proofs. It contains many exercises and examples arising from the applications in mechanics, physics, optics and, quantum mechanics.
| Author | : Fritz John |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 74 |
| Release | : 1990-07-01 |
| Genre | : Mathematics |
| ISBN | : 0821870017 |
This is the second volume in the University Lecture Series, designed to make more widely available some of the outstanding lectures presented in various institutions around the country. Each year at Lehigh University, a distinguished mathematical scientist presents the Pitcher Lectures in the Mathematical Sciences. This volume contains the Pitcher lectures presented by Fritz John in April 1989. The lectures deal with existence in the large of solutions of initial value problems for nonlinear hyperbolic partial differential equations. As is typical with nonlinear problems, there are many results and few general conclusions in this extensive subject, so the author restricts himself to a small portion of the field, in which it is possible to discern some general patterns. Presenting an exposition of recent research in this area, the author examines the way in which solutions can, even with small and very smooth initial data, ``blow up'' after a finite time. For various types of quasi-linear equations, this time depends strongly on the number of dimensions and the ``size'' of the data. Of particular interest is the formation of singularities for nonlinear wave equations in three space dimensions.
| Author | : Claudio Canuto |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 585 |
| Release | : 2007-09-23 |
| Genre | : Science |
| ISBN | : 3540307265 |
Since the publication of "Spectral Methods in Fluid Dynamics" 1988, spectral methods have become firmly established as a mainstream tool for scientific and engineering computation. The authors of that book have incorporated into this new edition the many improvements in the algorithms and the theory of spectral methods that have been made since then. This latest book retains the tight integration between the theoretical and practical aspects of spectral methods, and the chapters are enhanced with material on the Galerkin with numerical integration version of spectral methods. The discussion of direct and iterative solution methods is also greatly expanded.
