A Dressing Method in Mathematical Physics

A Dressing Method in Mathematical Physics
Author: Evgeny V. Doktorov
Publisher: Springer Science & Business Media
Total Pages: 413
Release: 2007-05-19
Genre: Science
ISBN: 1402061404

This monograph systematically develops and considers the so-called "dressing method" for solving differential equations (both linear and nonlinear), a means to generate new non-trivial solutions for a given equation from the (perhaps trivial) solution of the same or related equation. Throughout, the text exploits the "linear experience" of presentation, with special attention given to the algebraic aspects of the main mathematical constructions and to practical rules of obtaining new solutions.

Integrable Hamiltonian Hierarchies

Integrable Hamiltonian Hierarchies
Author: Vladimir Gerdjikov
Publisher: Springer
Total Pages: 645
Release: 2008-12-02
Genre: Science
ISBN: 3540770542

This book presents a detailed derivation of the spectral properties of the Recursion Operators allowing one to derive all the fundamental properties of the soliton equations and to study their hierarchies.

Nonlinear Systems and Their Remarkable Mathematical Structures

Nonlinear Systems and Their Remarkable Mathematical Structures
Author: Norbert Euler
Publisher: CRC Press
Total Pages: 367
Release: 2021-09-07
Genre: Mathematics
ISBN: 1000423301

The third volume in this sequence of books consists of a collection of contributions that aims to describe the recent progress in nonlinear differential equations and nonlinear dynamical systems (both continuous and discrete). Nonlinear Systems and Their Remarkable Mathematical Structures: Volume 3, Contributions from China just like the first two volumes, consists of contributions by world-leading experts in the subject of nonlinear systems, but in this instance only featuring contributions by leading Chinese scientists who also work in China (in some cases in collaboration with western scientists). Features Clearly illustrate the mathematical theories of nonlinear systems and its progress to both the non-expert and active researchers in this area Suitable for graduate students in Mathematics, Applied Mathematics and some of the Engineering sciences Written in a careful pedagogical manner by those experts who have been involved in the research themselves, and each contribution is reasonably self-contained

Nonlinear Dynamics and Applications

Nonlinear Dynamics and Applications
Author: Santo Banerjee
Publisher: Springer Nature
Total Pages: 1433
Release: 2022-10-06
Genre: Science
ISBN: 3030997928

This book covers recent trends and applications of nonlinear dynamics in various branches of society, science, and engineering. The selected peer-reviewed contributions were presented at the International Conference on Nonlinear Dynamics and Applications (ICNDA 2022) at Sikkim Manipal Institute of Technology (SMIT) and cover a broad swath of topics ranging from chaos theory and fractals to quantum systems and the dynamics of the COVID-19 pandemic. Organized by the SMIT Department of Mathematics, this international conference offers an interdisciplinary stage for scientists, researchers, and inventors to present and discuss the latest innovations and trends in all possible areas of nonlinear dynamics.

Glimpses of Soliton Theory

Glimpses of Soliton Theory
Author: Alex Kasman
Publisher: American Mathematical Soc.
Total Pages: 322
Release: 2010
Genre: Mathematics
ISBN: 0821852450

Glimpses of Soliton Theory addresses some of the hidden mathematical connections in soliton theory which have been revealed over the last half-century. It aims to convince the reader that, like the mirrors and hidden pockets used by magicians, the underlying algebro-geometric structure of soliton equations provides an elegant and surprisingly simple explanation of something seemingly miraculous. --

The Dynamical Projectors Method

The Dynamical Projectors Method
Author: Sergey Leble
Publisher: CRC Press
Total Pages: 398
Release: 2018-03-12
Genre: Science
ISBN: 1351107976

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

Horizons in World Physics

Horizons in World Physics
Author: Tori V. Lynch
Publisher: Nova Publishers
Total Pages: 298
Release: 2004
Genre: Science
ISBN: 9781594540639

This volume presents leading-edge research in physics from researchers around the world.

Trails in Modern Theoretical and Mathematical Physics

Trails in Modern Theoretical and Mathematical Physics
Author: Andrea Cintio
Publisher: Springer Nature
Total Pages: 321
Release: 2024-01-22
Genre: Science
ISBN: 3031449886

This book celebrates the life and work of the late Giovanni Morchio (1944–2021). It features scientific and anecdotal contributions written by his former colleagues, co-authors, and students, as well as senior scientists who were active witnesses to the dramatic advances in physics and in mathematics that took place during his 50-year-long career. The volume begins with a biographical introduction, detailing Giovanni Morchio’s life and his role as a physicist, mathematician, teacher, and scientist. The core of the book covers a vast spectrum of ideas, reflecting Dr Morchio’s scientific interests. Each chapter develops a specific topic of modern research, ranging from quantum mechanics and quantum field theory to additional themes such as the connection between general relativity and Newtonian gravitation. Every contribution provides a historical retrospective, a survey of advances, an outlook of future perspectives and challenges, and an updated bibliography. The last part collects the authors’ recollections of their professional and personal interactions with Dr Morchio, in recognition of his deep achievements, his exceptional pedagogical qualities, and his praiseworthy social and pro bono commitment. Authored by physicists of international calibre covering a broad range of subjects, the book will be a valuable reference for researchers and students of theoretical and mathematical physics.

Mathematical Physics II

Mathematical Physics II
Author: Enrico De Micheli
Publisher: MDPI
Total Pages: 182
Release: 2020-12-15
Genre: Mathematics
ISBN: 3039434950

The charm of Mathematical Physics resides in the conceptual difficulty of understanding why the language of Mathematics is so appropriate to formulate the laws of Physics and to make precise predictions. Citing Eugene Wigner, this “unreasonable appropriateness of Mathematics in the Natural Sciences” emerged soon at the beginning of the scientific thought and was splendidly depicted by the words of Galileo: “The grand book, the Universe, is written in the language of Mathematics.” In this marriage, what Bertrand Russell called the supreme beauty, cold and austere, of Mathematics complements the supreme beauty, warm and engaging, of Physics. This book, which consists of nine articles, gives a flavor of these beauties and covers an ample range of mathematical subjects that play a relevant role in the study of physics and engineering. This range includes the study of free probability measures associated with p-adic number fields, non-commutative measures of quantum discord, non-linear Schrödinger equation analysis, spectral operators related to holomorphic extensions of series expansions, Gibbs phenomenon, deformed wave equation analysis, and optimization methods in the numerical study of material properties.