This textbook covers the advanced application and techniques of electrodynamics. The book begins with an introduction to the topic, with basic notations and equations presented, before moving on to examine various topics such as electromagnetic waves in a vacuum, the theory of relativity (including the Lorentz transformation) and electromagnetic fields in matter. Dispersion and transport are discussed, along with wave interactions in types of plasma and metamaterials, before the problems of electromagnetism in continuous matter are reviewed, and boundary interactions are studied.

The second half of the book looks at the more advanced topics, including dielectric guides techniques, further metamaterial and plasma interactions (such as helicoidal phenomena), interactions involving conductivity and X-ray, and magnetic field dynamics. Condensed matter equations are covered along with more general matter relations, and an advanced study of the direct and inverse problems of electrodynamics closes the topic. Finally, advanced exercises are available in the final chapter.

This is an excellent learning tool for students studying electrodynamics courses, and serves as a robust resource for anyone involved in the field.

Key Features

The dynamical projectors method proves to reduce a multicomponent problem to the simplest one-component problem with its solution determined by specific initial or boundary conditions. Its universality and application in many different physical problems make it particularly useful in hydrodynamics, electrodynamics, plasma physics, and boundary layer problems. A great variety of underlying mechanisms are included making this book useful for those working in wave theory, hydrodynamics, electromagnetism, and applications.

"The authors developed a universal and elegant tool – dynamical projector method. Using this method for very complicated hydro-thermodynamic and electrodynamics problem settings, they were able to get a lot of interesting analytical results in areas where before often just numerical methods were applicable."

—L. A. Bordag, University of Applied Sciences Zittau/Görlitz, Zittau, Germany

"The book is intended for professionals working in various fields of linear and nonlinear mathematical physics, partial differential equations and theoretical physics. The book is written clearly, and in my opinion, its material will be useful and easy to understand for professionals and for students familiar with ordinary and partial differential equations."

—Sergey Dobrokhotov, Russian Academy of Sciences, Moscow, Russia

The dynamical projectors method proves to reduce a multicomponent problem to the simplest one-component problem with its solution determined by specific initial or boundary conditions. Its universality and application in many different physical problems make it particularly useful in hydrodynamics, electrodynamics, plasma physics, and boundary layer problems. A great variety of underlying mechanisms are included making this book useful for those working in wave theory, hydrodynamics, electromagnetism, and applications.

"The authors developed a universal and elegant tool – dynamical projector method. Using this method for very complicated hydro-thermodynamic and electrodynamics problem settings, they were able to get a lot of interesting analytical results in areas where before often just numerical methods were applicable."

—L. A. Bordag, University of Applied Sciences Zittau/Görlitz, Zittau, Germany

"The book is intended for professionals working in various fields of linear and nonlinear mathematical physics, partial differential equations and theoretical physics. The book is written clearly, and in my opinion, its material will be useful and easy to understand for professionals and for students familiar with ordinary and partial differential equations."

—Sergey Dobrokhotov, Russian Academy of Sciences, Moscow, Russia

This book addresses the peculiarities of nonlinear wave propagation in waveguides and explains how the stratification depends on the waveguide and confinement. An example of this is an optical fibre that does not allow light to pass through a density jump. The book also discusses propagation in the nonlinear regime, which is characterized by a specific waveform and amplitude, to demonstrate so-called solitonic behaviour. In this case, a wave may be strongly localized, and propagates with a weak change in shape. In the waveguide case there are additional contributions of dispersion originating from boundary or asymptotic conditions.

Offering concrete guidance on solving application problems, this essentially (more than twice) expanded second edition includes various aspects of guided propagation of nonlinear waves as well as new topics like solitonic behaviour of one-mode and multi-mode excitation and propagation and plasma waveguides, propagation peculiarities of electromagnetic waves in metamaterials, new types of dispersion, dissipation, electromagnetic waveguides, planetary waves and plasma waves interaction.The key feature of the solitonic behaviour is based on Coupled KdV and Coupled NS systems. The systems are derived in this book and solved numerically with the proof of stability and convergence. The domain wall dynamics of ferromagnetic microwaveguides  and Bloch waves in nano-waveguides are also included with some problems of magnetic momentum and charge transport.

This textbook covers the advanced application and techniques of electrodynamics. The book begins with an introduction to the topic, with basic notations and equations presented, before moving on to examine various topics such as electromagnetic waves in a vacuum, the theory of relativity (including the Lorentz transformation) and electromagnetic fields in matter. Dispersion and transport are discussed, along with wave interactions in types of plasma and metamaterials, before the problems of electromagnetism in continuous matter are reviewed, and boundary interactions are studied.

The second half of the book looks at the more advanced topics, including dielectric guides techniques, further metamaterial and plasma interactions (such as helicoidal phenomena), interactions involving conductivity and X-ray, and magnetic field dynamics. Condensed matter equations are covered along with more general matter relations, and an advanced study of the direct and inverse problems of electrodynamics closes the topic. Finally, advanced exercises are available in the final chapter.

This is an excellent learning tool for students studying electrodynamics courses, and serves as a robust resource for anyone involved in the field.

Key Features

The dynamical projectors method proves to reduce a multicomponent problem to the simplest one-component problem with its solution determined by specific initial or boundary conditions. Its universality and application in many different physical problems make it particularly useful in hydrodynamics, electrodynamics, plasma physics, and boundary layer problems. A great variety of underlying mechanisms are included making this book useful for those working in wave theory, hydrodynamics, electromagnetism, and applications.

"The authors developed a universal and elegant tool – dynamical projector method. Using this method for very complicated hydro-thermodynamic and electrodynamics problem settings, they were able to get a lot of interesting analytical results in areas where before often just numerical methods were applicable."

—L. A. Bordag, University of Applied Sciences Zittau/Görlitz, Zittau, Germany

"The book is intended for professionals working in various fields of linear and nonlinear mathematical physics, partial differential equations and theoretical physics. The book is written clearly, and in my opinion, its material will be useful and easy to understand for professionals and for students familiar with ordinary and partial differential equations."

—Sergey Dobrokhotov, Russian Academy of Sciences, Moscow, Russia

The dynamical projectors method proves to reduce a multicomponent problem to the simplest one-component problem with its solution determined by specific initial or boundary conditions. Its universality and application in many different physical problems make it particularly useful in hydrodynamics, electrodynamics, plasma physics, and boundary layer problems. A great variety of underlying mechanisms are included making this book useful for those working in wave theory, hydrodynamics, electromagnetism, and applications.

"The authors developed a universal and elegant tool – dynamical projector method. Using this method for very complicated hydro-thermodynamic and electrodynamics problem settings, they were able to get a lot of interesting analytical results in areas where before often just numerical methods were applicable."

—L. A. Bordag, University of Applied Sciences Zittau/Görlitz, Zittau, Germany

"The book is intended for professionals working in various fields of linear and nonlinear mathematical physics, partial differential equations and theoretical physics. The book is written clearly, and in my opinion, its material will be useful and easy to understand for professionals and for students familiar with ordinary and partial differential equations."

—Sergey Dobrokhotov, Russian Academy of Sciences, Moscow, Russia

This book addresses the peculiarities of nonlinear wave propagation in waveguides and explains how the stratification depends on the waveguide and confinement. An example of this is an optical fibre that does not allow light to pass through a density jump. The book also discusses propagation in the nonlinear regime, which is characterized by a specific waveform and amplitude, to demonstrate so-called solitonic behaviour. In this case, a wave may be strongly localized, and propagates with a weak change in shape. In the waveguide case there are additional contributions of dispersion originating from boundary or asymptotic conditions.

Offering concrete guidance on solving application problems, this essentially (more than twice) expanded second edition includes various aspects of guided propagation of nonlinear waves as well as new topics like solitonic behaviour of one-mode and multi-mode excitation and propagation and plasma waveguides, propagation peculiarities of electromagnetic waves in metamaterials, new types of dispersion, dissipation, electromagnetic waveguides, planetary waves and plasma waves interaction.The key feature of the solitonic behaviour is based on Coupled KdV and Coupled NS systems. The systems are derived in this book and solved numerically with the proof of stability and convergence. The domain wall dynamics of ferromagnetic microwaveguides  and Bloch waves in nano-waveguides are also included with some problems of magnetic momentum and charge transport.