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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.
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