Nayfeh A.H. Perturbation Methods

Cambridge University Press, 2011,362 p. The field of nonlinear dispersive waves has developed enormously since the work of Stokes, Boussinesq and Korteweg-de Vries (KdV) in the nineteenth century. In the 1960s, researchers developed effective asymptotic methods for deriving nonlinear wave equations, such as the KdV equation, governing a broad class of physical phenomena that admit special solutions including those commonly known as solitons. This...

Springer, 2007, 304 pages This text gives a detailed account of various techniques that are used in the study of dynamics of continuous systems, near as well as far from equilibrium. The analytic methods covered include diagrammatic perturbation theory, various forms of the renormalization group and self-consistent mode coupling. Dynamic critical phenomena near a second order phase transition, phase ordering dynamics, dynamics of surface growth...

Springer, 2009. - 264 pages. Alessandra Celletti’s proposed book presents classical celestial mechanics and its interplay with dynamical systems in a way that would be suitable for advance level undergraduate students as well as postgraduate students and researchers. First she uses paradigmatic models, such as the logistic map or the standard map, to introduce the reader to the concepts of order, chaos, invariant curves, cantori, etc. The main n...

Springer, 2000. - 338 pages. Beginning with ordinary language models or realistic mathematical models of physical or biological phenomena, the author derives tractable mathematical models that are amenable to further mathematical analysis or to elucidating computer simulations. For the most part, derivations are based on perturbation methods. Because of this, the majority of the text is devoted to careful derivations of implicit function theorem...

2 edition. Cambridge University Press, 2004. 388 p. ISBN:0521821509 The time variability of many natural and social phenomena is not well described by standard methods of data analysis. However, nonlinear time series analysis uses chaos theory and nonlinear dynamics to understand seemingly unpredictable behavior. The results are applied to real data from physics, biology, medicine, and engineering in this volume. Researchers from all experiment...

Cambridge University Press, 1991. - 377 Pages. Surveying both theoretical and experimental aspects of chaotic behavior, this book presents chaos as a model for many seemingly random processes in nature. Basic notions from the theory of dynamical systems, bifurcation theory and the properties of chaotic solutions are then described and illustrated by examples. A review of numerical methods used both in studies of mathematical models and in the i...

Wiley-VCH, 1993. - 536 Pages. Similarities, differences, advantages and limitations of perturbation techniques are pointed out concisely. The techniques are described by means of examples that consist mainly of algebraic and ordinary differential equations. Each chapter contains a number of exercises.

Wiley, 1995. - 720 pages. Nonlinear Oscillations is a self-contained and thorough treatment of the vigorous research that has occurred in nonlinear mechanics since 1970. The book begins with fundamental concepts and techniques of analysis and progresses through recent developments and provides an overview that abstracts and introduces main nonlinear phenomena. It treats systems having a single degree of freedom, introducing basic concepts and an...

Park К. С. An improved stiffly stable method for direct integration of nonlinear structural dynamic equations. Journal of Applied Mechanics, ASME, Vol.42, pp. 464-470. ( June 1975 -- Volume 42, Issue 2, 464 (7 pages) doi:10.1115/ 1.3423600. ) ABSTRACT Author(s): K. C. Park Structural Mechanics Laboratory, Lockheed Palo Alto Research Laboratory, Palo Alto, Calif. The behavior of linear multistep methods has been evaluated for application to struc...

Springer-Verlag Berlin, 2010, 298 pages Linear, Time-varying Approximations to Nonlinear Dynamical Systems introduces a new technique for analysing and controlling nonlinear systems. This method is general and requires only very mild conditions on the system nonlinearities, setting it apart from other techniques such as those – well-known – based on differential geometry. The authors cover many aspects of nonlinear systems including stability t...