This textbook is devoted to nonlinear physics, using the asymptotic perturbation method as a mathematical tool. The theory is developed systematically, starting with nonlinear oscillators, limit cycles and their bifurcations, followed by iterated nonlinear maps, continuous systems, nonlinear partial differential equations (NPDEs) and culminating with infinite-period bifurcation in the nonlinear Schrodinger equation and fractal and chaotic solutions in NPDEs. A remarkable feature of the book is its emphasis on applications. It offers several examples, and the scientific background is explained at an elementary level and closely integrated with the mathematical theory. In addition, it is ideal for an introductory course at the senior or first-year graduate level.

Cohesive overview of powerful mathematical methods to solve differential equations in physics Asymptotic Perturbation Methods for Nonlinear Differential Equations in Physics addresses nonlinearity in various fields of physics from the vantage point of its mathematical description in the form of nonlinear partial differential equations and presents a unified view on nonlinear systems in physics by providing a common framework to obtain approximate solutions to the respective nonlinear partial differential equations based on the asymptotic perturbation method. Aside from its complete coverage of a complicated topic, a noteworthy feature of the book is the emphasis on applications. There are several examples included throughout the text, and, crucially, the scientific background is explained at an elementary level and closely integrated with the mathematical theory to enable seamless reader comprehension. To fully understand the concepts within this book, the prerequisites are multivariable calculus and introductory physics. Written by a highly qualified author with significant accomplishments in the field, Asymptotic Perturbation Methods for Nonlinear Differential Equations in Physics covers sample topics such as: Application of the various flavors of the asymptotic perturbation method, such as the Maccari method to the governing equations of nonlinear system Nonlinear oscillators, limit cycles, and their bifurcations, iterated nonlinear maps, continuous systems, and nonlinear partial differential equations (NPDEs) Nonlinear systems, such as the van der Pol oscillator, with advanced coverage of plasma physics, quantum mechanics, elementary particle physics, cosmology, and chaotic systems Infinite-period bifurcation in the nonlinear Schrodinger equation and fractal and chaotic solutions in NPDEs Asymptotic Perturbation Methods for Nonlinear Differential Equations in Physics is ideal for an introductory course at the senior or first year graduate level. It is also a highly valuable reference for any professional scientist who does not possess deep knowledge about nonlinear physics.

The mid-infrared domain is a promising optical domain because it holds two transparency atmospheric windows, as well as the fingerprint of many chemical compounds. Quantum cascade lasers (QCLs) are one of the available sources in this domain and have already been proven useful for spectroscopic applications and free-space communications. This thesis demonstrates how to implement a private free-space communication relying on mid-infrared optical chaos and this requires an accurate cartography of non-linear phenomena in quantum cascade lasers. This private transmission is made possible by the chaos synchronization of two twin QCLs. Chaos in QCLs can be generated under optical injection or external optical feedback. Depending on the parameters of the optical feedback, QCLs can exhibit several non-linear phenomena in addition to chaos. Similarities exist between QCLs and laser diodes when the chaotic dropouts are synchronized with an external modulation, and this effect is known as the entrainment phenomenon. With a cross-polarization reinjection technique, QCLs can generate all-optical square-waves. Eventually, it is possible to trigger optical extreme events in QCLs with tilted optical feedback. All these experimental results allow a better understanding of the non-linear dynamics of QCLs and will extend the potential applications of this kind of semiconductor lasers.

This textbook gives an instructive view of solitons and their applications for advanced students of physics.

Provides the state-of-the-art of the physics of granular media for graduate students and researchers in physics, applied mathematics and engineering.

With this book, we aim to capture different perspectives of researchers on nonlinear optics and optical devices and we intend to cover the latest developments in optics from theoretical, numerical, and experimental aspects. The eleven selected chapters cover a variety of topics related to nonlinear optics including bright, dark, kink solitary waves in various media, magnetic solitons, lattice solitons, rogue-waves, solid-state lasers, laser cladding, optical sensors, optical vortices, and molecular switches. The book is intended to draw the attention of scientists in academia, as well as researchers and engineers in industry, since the field has a significant potential for the production and design of novel optical devices and other technological applications.