Nonlinear systems

Preface / Nonlinear Systems: General: Nonlinear dynamics: From theory to technology / Soliton Systems and Integrability: Geometry of Dirac structures, integrability and Lax-Lenard principle / Hirota derivatives, vertex operators and Plucker coordinates / Backlund transformations, quantum inverse problem and Q-operator / Completely integrable soliton models in resonant and nonresonant optical fibres / Backlund transformation for restricted flows / Oblique and parallel propagation of electromagnetic soliton in ferromagnetic medium / Nonlinear Differential and Difference Equations: Solutions : Nonconservative products in quasilinear hyperbolic systems / A new reduction of the nonplanar Burgers equation and exact analysis of the reduced ordinary differential equation / Nonlocal Cauchy problem for nonlinear differential equations in Banach spaces / Oscillation of solutions of forced nonlinear neutral difference equations of higher order / Existence of mild solutions of nonlinear functional integro - differential equations of neutral type / Oscillation of solutions of forced nonlinear second order difference equations/ Discrete Nonlinear Systems: Integrability: An invariant norm of nonlinear Hamiltonian systems / A panorama of the special solutions of the Painleve equations / Discrete nonlinear systems: Some recent developments / A Nevanlinna theory approach to the integrability of discrete systems / Classical and Quantum Chaos: Controlling chaos with threshold mechanisms / Diffusion in periodically driven damped and undamped pendulum / Scaling indices and dynamical states of 1-d discrete systems / Intermittency and multifractality in iterated function systems / Quantum theory of the chaotic ionization of highly excited helium atoms / List of contributors

Covers a range of topics in nonlinear science including those like Solitons and Chaos sharing common mathematical notions and investigation techniques. In this book, contributions represent status of important nonlinear theories in various areas of applied mathematics and mathematical physics providing a picture of areas with their applications.