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Nonlinear Waves and Solitons on Contours and Closed Surfaces

  • Book
  • © 2022

Overview

Authors:
  1. Andrei Ludu

    1. Department of Mathematics, Embry-Riddle Aeronautical University, Daytona Beach, USA

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  • Newly includes recent work on motion of solitons and of surfaces as well as 3D waves
  • Provides the necessary mathematical framework for treating the manifolds considered with relevant notions from topology
  • Applies the theory to many concrete examples appearing in the physical and related sciences

Part of the book series: Springer Series in Synergetics (SSSYN)

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Table of contents (19 chapters)

  1. Front Matter

    Pages i-xxxii
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  2. Introduction

    • Andrei Ludu
    Pages 1-20

  3. Mathematical Prerequisites

    1. Front Matter

      Pages 21-21
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    2. Topology and Algebra

      • Andrei Ludu
      Pages 23-39

    3. Vector Fields, Differential Forms, and Derivatives

      • Andrei Ludu
      Pages 41-88

    4. The Importance of the Boundary

      • Andrei Ludu
      Pages 89-96

  4. Curves and Surfaces

    1. Front Matter

      Pages 97-97
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    2. Geometry of Curves

      • Andrei Ludu
      Pages 99-116

    3. Geometry of Surfaces

      • Andrei Ludu
      Pages 117-151

    4. Motion of Curves and Solitons

      • Andrei Ludu
      Pages 153-182

    5. Theory of Motion of Surfaces

      • Andrei Ludu
      Pages 183-200

  5. Solitons and Nonlinear Waves on Closed Curves and Surfaces

    1. Front Matter

      Pages 201-202
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    2. Kinematics of Fluids

      • Andrei Ludu
      Pages 203-247

    3. Hydrodynamics

      • Andrei Ludu
      Pages 249-285

    4. Nonlinear Surface Waves in One Dimension

      • Andrei Ludu
      Pages 287-323

    5. Nonlinear Surface Waves in Two Dimensions

      • Andrei Ludu
      Pages 325-353

    6. Dynamics of Two-Dimensional Fluid in Bounded Domain via Conformal Variables (A. Chernyavsky and S. Dyachenko)

      • Andrei Ludu
      Pages 355-370

    7. Nonlinear Surface Waves in Three Dimensions

      • Andrei Ludu
      Pages 371-439

    8. Other Special Nonlinear Compact Systems

      • Andrei Ludu
      Pages 441-454

  6. Physical Nonlinear Systems at Different Scales

    1. Front Matter

      Pages 455-455
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Keywords

About this book

This new edition has been thoroughly revised, expanded and contain some updates function of the novel results and shift of scientific interest in the topics. The book has a Foreword by Jerry L. Bona and Hongqiu Chen. The book is an introduction to nonlinear waves and soliton theory in the special environment of compact spaces such a closed curves and surfaces and other domain contours. It assumes familiarity with basic soliton theory and nonlinear dynamical systems.

The first part of the book introduces the mathematical concept required for treating the manifolds considered, providing relevant notions from topology and differential geometry. An introduction to the theory of motion of curves and surfaces - as part of the emerging field of contour dynamics - is given.

The second and third parts discuss the modeling of various physical solitons on compact systems, such as filaments, loops and drops made of almost incompressible materials thereby intersecting with a large number of physical disciplines from hydrodynamics to compact object astrophysics.

This book is intended for graduate students and researchers in mathematics, physics and engineering.


Reviews

“The interested reader can find a sufficiently readable exposition of the basic ideas of this topic, taste the implementation of a wide range of analytical and numerical methods for obtaining new results … and enjoy a comprehensive review of their applications. ... I would say that the third edition of the book Nonlinear Waves and Solitons on Contours and Closed Surfaces by Andrei Ludu is worth reading for everyone interested in the exciting theory of solitary waves … .” (Vassil M. Vassilev, Journal of Geometry and Symmetry in Physics JGSP, Vol. 66, 2023)

Authors and Affiliations

  • Department of Mathematics, Embry-Riddle Aeronautical University, Daytona Beach, USA

    Andrei Ludu

About the author

Dr. A. Ludu graduated in 1980 the MS Program in Theoretical Physics and Mathematics from University of Bucharest and he had received his Ph. D. in Physics in 1989 from the “H. Hulubei National Institute of Physics” in Bucharest-Magurele, Romania with a thesis on group transformations approach on hot and dense plasma. He worked for the national H Program on ultrahigh magnetic fields as a senior researcher in this Institute until 1985, after which he joined the Dept. Theoretical Physics of University of Bucharest as Associate Professor, until 1996. Between 1986 and 2001 he was postdoctoral researcher at Louisiana State University in Baton Rouge, and he joined Northwestern State University as Professor of Physics until 2011. At present he is Professor of Mathematics and Director of the Wave Lab in the Dept. of Mathematics at Embry-Riddle Aeronautical University in Daytona Beach. He published more than 80 peer reviewed paper in scientific journals and 4 books on the topics of solitons andnonlinear systems, applied differential geometry in physics, quantum groups, fluid dynamics, nuclear theory, biophysics, ultra-high energy density systems and wavelets. He was invited to work and give talks at prestigious centers of research including Los Alamos Natl. Lab, ICTP Trieste, Antwerp University, Université Libre de Bruxelles,  US Navy Research Labs, Plymouth University, Trinity College, Niels Bohr Institute, Abo Akademi, Dalian University of Technology, etc. He was guest professor for more than ten years at J. Liebig University in Giessen and Goethe University in Frankfurt/Main, Germany. He was awarded the Mildred Hart Bailey Research Award and he is honorary member of several professional associations and science groups. In 1992 he predicted the existence of shape solitons orbiting on the surface of spheres (rotons). These predictions were continuously confirmed experimentally in systems like heavy nuclei collisions, flat electron drops, liquid drops and Leidenfrost drops and tori between 2007 and present.  Dr. Ludu is married since 1980 to Maria, who is Professor of Mathematics at Embry-Riddle, and they have a daughter Delia, artist and graphic designer. He is VFR private pilot and practiced AMA enduro motorcycling, radio ham, and art photography.   

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