Nonlinear Systems and Their Remarkable Mathematical Structures, Volume II: 1st Edition (Hardback) book cover

Nonlinear Systems and Their Remarkable Mathematical Structures, Volume II

1st Edition

Edited by Norbert Euler, Maria Clara Nucci

CRC Press

523 pages | 51 Color Illus.

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Hardback: 9780367208479
pub: 2019-11-18
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Description

Nonlinear Systems and Their Remarkable Mathematical Structures, Volume II is written in a careful pedagogical manner by experts from the field of nonlinear differential equations and nonlinear dynamical systems (both continuous and discrete). This book aims to clearly illustrate the mathematical theories of nonlinear systems and its progress to both non-experts and active researchers in this area.

Just like the first volume, this book is suitable for graduate students in Mathematics, Applied Mathematics and Engineering sciences, as well as for researchers in the subject of differential equations and dynamical systems.

Features

  • Collects contributions on recent advances in the subject of nonlinear systems
  • Aims to make the advanced mathematical methods accessible to the non-experts
  • Suitable for a broad readership including researchers and graduate students in mathematics and applied mathematics

Table of Contents

Part A: Integrability, Lax Pairs and Symmetry. A1. Reciprocal transformations and their role in the integrability and classification of PDEs. A2. Contact Lax pairs and associated (3+1)-dimensional integrable dispersionless systems. A3. Lax Pairs for Edge-constrained Boussinesq Systems of Partial Difference Equations. A4. Lie point symmetries of delay ordinary differential equations. A5. The symmetry approach to integrability: recent advances. A6. Evolution of the concept of λ--symmetry and main applications. A7. Heir-equations for partial dfferential equations: a 25-year review. Part B: Algebraic and Geometric Methods. B1. Coupled nonlinear Schrodinger equations: spectra and instabilities of plane waves. B2. Rational solutions of Painleve systems. B3. Cluster algebras and discrete integrability. B4. A review of elliptic difference Painleve equations. B5. Linkage mechanisms governed by integrable deformations of discrete space curves. B6. The Cauchy problem of the Kadomtsev-Petviashvili hierarchy and infinite-dimensional groups. B7. Wronskian solutions of integrable systems. Part C: Applications. C1. Global gradient catastrophe in a shallow water model: evolution unfolding by stretched coordiates. C2. Vibrations of an elastic bar, isospectral deformations, and modified Camassa-Holm equations. C3. Exactly solvable (discrete) quantum mechanics and new orthogonal polynomials.

About the Editors

Norbert Euler is currently a visiting Research Professor at the "Centro Internacional de Ciencias AC" in Cuernavaca, Mexico. He has been a Professor of Mathematics at Luleå University of Technology in Sweden, where he was teaching and researching for almost 23 years until April 2019. His main research interests are in the subject of Nonlinear Mathematical Physics, in particular nonlinear ordinary and partial differential equations and integrable systems, and has published over 70 peer reviewed research articles and co-authored several books. He is involved in editorial work for some journals, and he is the Editor-in-chief of the Journal of Nonlinear Mathematical Physics since 1997.

Maria Clara Nucci is Associate Professor of Mathematical Physics at University of Perugia, where she graduated in Mathematics summa cum laude. Between 1986 and 1991 she was Visiting Assistant Professor at Georgia Institute of Technology, Atlanta (U.S.A.). She has also been invited at universities in Australia, Canada, France, Germany, Greece, Sweden, U.K., U.S.A. She has presented her research at many International Congresses and Workshops. From 1995 to 2009 she was Associate Editor of Journal of Mathematical Analysis and Applications, and since 2003 has been a Member of the Editorial Board of Journal of Nonlinear Mathematical Physics. She is author or co-author of more than 100 publications, and has wide ranging research interests, from fluid to rigid body mechanics, from epidemiology to astrophysics, from history of mathematics to quantum mechanics.

Subject Categories

BISAC Subject Codes/Headings:
MAT000000
MATHEMATICS / General