This volume provides an in-depth treatment of several equations and systems of mathematical physics, describing the propagation and interaction of nonlinear waves as different modifications of these: the KdV equation, Fornberg-Whitham equation, Vakhnenko equation, Camassa-Holm equation, several versions of the NLS equation, Kaup-Kupershmidt equation, Boussinesq paradigm, and Manakov system, amongst others, as well as symmetrizable quasilinear hyperbolic systems arising in fluid dynamics.Readers not familiar with the complicated methods used in the theory of the equations of mathematical physics (functional analysis, harmonic analysis, spectral theory, topological methods, a priori estimates, conservation laws) can easily be acquainted here with different solutions of some nonlinear PDEs written in a sharp form (waves), with their geometrical visualization and their interpretation. In many cases, explicit solutions (waves) having specific physical interpretation (solitons, kinks, peakons, ovals, loops, rogue waves) are found and their interactions are studied and geometrically visualized. To do this, classical methods coming from the theory of ordinary differential equations, the dressing method, Hirota's direct method and the method of the simplest equation are introduced and applied. At the end, the paradifferential approach is used.This volume is self-contained and equipped with simple proofs. It contains many exercises and examples arising from the applications in mechanics, physics, optics and, quantum mechanics.

This book deals with equations of mathematical physics as the different modifications of the KdV equation, the Camassa-Holm type equations, several modifications of Burger's equation, the Hunter-Saxton equation and others. The equations originate from physics but are proposed here for their investigation via purely mathematical methods in the frames of university courses. More precisely, the authors propose classification theorems for the traveling wave solutions for a sufficiently large class of third order nonlinear PDE when the corresponding profiles develop different kind of singularities (cusps, peaks). The orbital stability of the periodic solutions of traveling type for mKdV equations are also studied. Of great interest too is the interaction of peakon type solutions of the Camassa-Holm equation and the solvability of the classical and generalized Cauchy problem for the Hunter-Saxton equation. The Riemann problem for special systems of conservation laws and the corresponding d-shocks are also considered. At the end of the book the authors study the interaction of two piecewise smooth waves in the case of two space variables and they verify the appearance of logarithmic singularities. As it concerns numerical methods in the case of periodic waves the authors apply Cellular Neural Network (CNN) approach.

This contributed volume offers practical solutions and design-, modeling-, and implementation-related insights that address current research problems in memristors, memristive devices, and memristor computing. The book studies and addresses related challenges in and proposes solutions for the future of memristor computing. State-of-the-art research on memristor modeling, memristive interconnections, memory circuit architectures,  software simulation tools, and applications of memristors in computing are presented. Utilising contributions from numerous experts in the field, written in clear language and illustrated throughout, this book is a comprehensive reference work. Memristor Computing Systems explains memristors and memristive devices in an accessible way for graduate students and researchers with a basic knowledge of electrical and control systems engineering, as well as prompting further research for more experienced academics.

This book convenes peer-reviewed, selected papers presented at the Ninth International Conference New Trends in the Applications of Differential Equations in Sciences (NTADES) held in Sozopol, Bulgaria, June 17–20, 2022. The works are devoted to many applications of differential equations in different fields of science. A number of phenomena in nature (physics, chemistry, biology) and in society (economics) result in problems leading to the study of linear and nonlinear differential equations, stochastic equations, statistics, analysis, numerical analysis, optimization, and more. The main topics are presented in the five parts of the book - applications in mathematical physics, mathematical biology, financial mathematics, neuroscience, and fractional analysis. In this volume, the reader will find a wide range of problems concerning recent achievements in both theoretical and applied mathematics. The main goal is to promote the exchange of new ideas and research between scientists, who develop and study differential equations, and researchers, who apply them for solving real-life problems. The book promotes basic research in mathematics leading to new methods and techniques useful for applications of differential equations. The NTADES 2022 conference was organized in cooperation with the Society of Industrial and Applied Mathematics (SIAM), the major international organization for Industrial and Applied Mathematics and for the promotion of interdisciplinary collaboration between applied mathematics and science, engineering, finance, and neuroscience.

This contributed volume offers practical solutions and design-, modeling-, and implementation-related insights that address current research problems in memristors, memristive devices, and memristor computing. The book studies and addresses related challenges in and proposes solutions for the future of memristor computing. State-of-the-art research on memristor modeling, memristive interconnections, memory circuit architectures, software simulation tools, and applications of memristors in computing are presented. Utilising contributions from numerous experts in the field, written in clear language and illustrated throughout, this book is a comprehensive reference work. Memristor Computing Systems explains memristors and memristive devices in an accessible way for graduate students and researchers with a basic knowledge of electrical and control systems engineering, as well as prompting further research for more experienced academics.

This book presents a study of neuroscience models and natural phenomena, such as tsunami waves and tornados. The first part discusses various mathematical models of tsunamis, including the Korteweg-de Vries equation, shallow water equations and the Camassa-Holm equation (CH). In order to study the dynamics of these models, the text uses the Cellular Nonlinear Networks (CNN) approach to discretize the governing equation using a suitable mathematical grid. The second part discusses some of the models arising in the field of neuroscience. It examines the Fitzhugh-Nagumo systems, which are very important for understanding the qualitative nature of nerve impulse propagation.The volume will be of interest to a wide-ranging audience, including PhD students, mathematicians, physicists, engineers and specialists in the domain of nonlinear waves and their applications.