الصفحة 1
الصفحة 1
NonlinearWaves and Solitons on Contours and Closed Surfaces
The present volume is an introduction to nonlinear waves and soliton theory in the special environment of compact spaces such a closed curves and surfaces and other domain contours. It assumes familiarity with basic soliton theory and nonlinear dynamical systems.
Nonlinear Partial Differential Equations for Scientists and Engineers
This expanded and revised second edition is a comprehensive and systematic treatment of linear and nonlinear partial differential equations and their varied applications. Building upon the successful material of the first book, this edition contains updated modern examples and applications from areas of fluid dynamics, gas dynamics, plasma physics, nonlinear dynamics, quantum mechanics, nonlinear optics, acoustics, and wave propagation. Methods and properties of solutions are presented, along with their physical significance, making the book more useful for a diverse readership.
Introduction to Soliton Theory : Applications to Mechanics
This monograph provides the application of soliton theory to solve certain problems selected from the fields of mechanics. The present monograph is not a simple translation of its predecessor appeared in Publishing House of the Romanian Academy in 2002. Improvements outline the way in which the soliton theory is applied to solve some engineering problems. The book addresses concrete resolution methods of certain problems such as the motion of thin elastic rod, vibrations of initial deformed thin elastic rod, the coupled pendulum oscillations, dynamics of left ventricle, transient flow of blood in arteries, the subharmonic waves generation in a piezoelectric plate with Cantor-like structure, and some problems related to Tzitzeica surfaces. This comprehensive study enables the readers to make connections between the soliton physical phenomenon and some partical, engineering problems.
Integrable Hamiltonian Hierarchies : Spectral and Geometric Methods
This book presents a detailed derivation of the spectral properties of the Recursion Operators allowing one to derive all the fundamental properties of the soliton equations and to study their Hamiltonian hierarchies. Thus it is demonstrated that the inverse scattering method for solving soliton equations is a nonlinear generalization of the Fourier transform. The book brings together the spectral and the geometric approaches and as such will be useful to a wide readership: from researchers in the field of nonlinear completely integrable evolution equations to graduate and post-graduate students.
High-dimensional chaotic and attractor systems : A comprehensive introduction
If we try to describe real world in mathematical terms, we will see that real life is very often a high–dimensional chaos. Sometimes, by ‘pushing hard’, we manage to make order out of it; yet sometimes, we need simply to accept our life as it is. To be able to still live successfully, we need tounderstand, predict, and ultimately control this high–dimensional chaotic dynamics of life. This is the main theme of the present book.
Hamiltonian Methods in the Theory of Solitons
The main characteristic of this now classic exposition of the inverse scattering method and its applications to soliton theory is its consistent Hamiltonian approach to the theory. The nonlinear Schrödinger equation, rather than the (more usual) KdV equation, is considered as a main example.
Fuchsian Reduction : Applications to Geometry, Cosmology, and Mathematical Physics
Fuchsian reduction is a method for representing solutions of nonlinear PDEs near singularities. The technique has multiple applications including soliton theory, Einstein's equations and cosmology, stellar models, laser collapse, conformal geometry and combustion. Developed in the 1990s for semilinear wave equations, Fuchsian reduction research has grown in response to those problems in pure and applied mathematics where numerical computations fail.
Emergent Nonlinear Phenomena in Bose-Einstein Condensates : Theory and Experiment
This book, written by experts in the fields of atomic physics and nonlinear science, consists of reviews of the current state of the art at the interface of these fields, as is exemplified by the modern theme of Bose-Einstein condensates. Topics covered include bright, dark, gap and multidimensional solitons; vortices; vortex lattices; optical lattices; multicomponent condensates; manipulation of condensates; mathematical methods/rigorous results; and aspects beyond the mean field approach. A distinguishing feature of the contents is the detailed incorporation of both the experimental and theoretical viewpoints through subsections of the relevant chapters.
Dissipative Solitons : From Optics to Biology and Medicine
The dissipative soliton concept is a fundamental extension of the concept of solitons in conservative and integrable systems. It includes ideas from three major sources, namely standard soliton theory developed since the 1960s, nonlinear dynamics theory, and Prigogine's ideas of systems far from equilibrium. These three sources also correspond to the three component parts of this novel paradigm. This book explains the above principles in detail and gives the reader various examples from optics, biology and medicine. These include laser systems, optical transmission lines, cortical networks, models of muscle contraction, localized vegetation structures and waves in brain tissues.
Dissipative Solitons
This volume is devoted to the exciting topic of dissipative solitons, i.e. pulses or spatially localised waves in systems exhibiting gain and loss. Examples are laser systems, nonlinear resonators and optical transmission lines. The physical principles and mathematical concepts are explained in a clear and concise way, suitable for students and young researchers. The similarities and differences in the notion of a soliton between dissipative systems and Hamiltonian and integrable systems are discussed, and many examples are given. The contributions are written by the world's leading experts in the field, making it a unique exposition of this emerging topic.
Computer Algebra Recipes : An Advanced Guide to Scientific Modeling
The text is built around a large number of computer algebra worksheets or "recipes" that have been designed using MAPLE to provide tools for problem solving and to stimulate critical thinking.
Chiral Soliton Models for Baryons
This concise research monograph introduces and reviews the concept of chiral soliton models for baryons. In these models, baryons emerge as (topological) defects of the chiral field. The many applications shed light on a number of bayron properties, ranging from static properties via nucleon resonances and deep inelastic scattering to even heavy ion collisions. As far as possible, the theoretical investigations are confronted with experiment. Conceived to bridge the gap between advanced graduate textbooks and the research literature, this volume also features a number of appendices to help nonspecialist readers to follow in more detail some of the calculations in the main text.
Bilinear integrable systems : From classical to quantum, continuous to discrete ; Proceedings of the NATO Advanced Research Workshop on Bilinear Integrable Systems: From Classical to Quantum, Continuous to Discrete St. Petersburg, Russia, 15-19 September 2002
Trained as a physicistin his home university Kyushu University, Professor Hirota earned his PhD in’61 at Northwestern University with Professor Siegert in the field of “QuantumStatistical mechanics”. He wrote a widely appreciated Doctoral dissertation on“Functional Integral representation of the grand partition function”. As a youngresearcher, he entered the RCA Company in Tokyo to do research on semi-conductor plasmas. Professor Hirota was led to model the Toda lattice as a non-linear networkof ladder-type LC circuits. The self-dual case led to equations very reminiscentof the Sine-Gordon equation, with much the same features (existence of onesoliton, soliton-soliton interaction, etc)
A Dressing Method in Mathematical Physics
The monograph is devoted to the systematic presentation of the so called "dressing method" for solving differential equations (both linear and nonlinear) of mathematical physics. The essence of the dressing method consists in a generation of new non-trivial solutions of a given equation from (maybe trivial) solution of the same or related equation.
