Nonlinear Systems, Vol. 1

Mathematical Theory and Computational Methods

  • Victoriano Carmona
  • Jesús Cuevas-Maraver
  • Fernando Fernández-Sánchez
  • Elisabeth García- Medina

Part of the Understanding Complex Systems book series (UCS)

Table of contents

  1. Front Matter
    Pages i-xv
  2. Bifurcation Analysis

    1. Front Matter
      Pages 1-1
    2. Antonio Algaba, M. Cinta Domínguez-Moreno, Manuel Merino, Alejandro J. Rodríguez-Luis
      Pages 3-36
    3. Antonio Algaba, Natalia Fuentes, Estanislao Gamero, Cristóbal García
      Pages 37-65
    4. Mathieu Desroches, Soledad Fernández-García, Martin Krupa, Rafel Prohens, Antonio E. Teruel
      Pages 67-86
  3. Wave Equations

    1. Front Matter
      Pages 87-87
    2. Jesús Cuevas-Maraver, Nabile Boussaïd, Andrew Comech, Ruomeng Lan, Panayotis G. Kevrekidis, Avadh Saxena
      Pages 89-143
    3. Angel Paredes, Humberto Michinel
      Pages 145-174
    4. Piotr Rozmej, Anna Karczewska
      Pages 175-205
    5. Francisco R. Villatoro
      Pages 207-240
  4. Differential and Difference Equations

    1. Front Matter
      Pages 241-241
    2. Antonio Algaba, Isabel Checa, Cristóbal García
      Pages 243-267
    3. Luca Salasnich, Andrea Bonato, Fabio Sattin
      Pages 295-313
  5. Computational Methods

    1. Front Matter
      Pages 315-315
    2. Antonio Cordoba, Christian Castillejo, Juan J. García-Machado, Ana M. Lara
      Pages 317-338
    3. Francisco Jiménez-Morales, José Luis Guisado, José Manuel Guerra
      Pages 405-422
  6. Back Matter
    Pages 423-424

About this book


This book is part of a two volume set which presents the analysis of nonlinear phenomena as a long-standing challenge for research in basic and applied science as well as engineering. It discusses nonlinear differential and differential equations, bifurcation theory for periodic orbits and global connections. The integrability and reversibility of planar vector fields and theoretical analysis of classic physical models are sketched.

This first volume concentrates on the mathematical theory and computational techniques that are essential for the study of nonlinear science, a second volume deals with real-world nonlinear phenomena in condensed matter, biology and optics.


Nonlinear Differential and Difference Equations Normal Forms for Planar Systems Local and Global Bifurcations Laser Dynamics Gravitational Waves Classical Models in Science Nonlinear Dirac Equation

Editors and affiliations

  • Victoriano Carmona
    • 1
  • Jesús Cuevas-Maraver
    • 2
  • Fernando Fernández-Sánchez
    • 3
  • Elisabeth García- Medina
    • 4
  1. 1.Departamento de Matemática Aplicada IIUniversidad de SevillaSevillaSpain
  2. 2.Departamento de Física Aplicada IUniversidad de SevillaSevillaSpain
  3. 3.Departamento de Matemática Aplicada IIUniversidad de SevillaSevillaSpain
  4. 4.Departamento de Matemática Aplicada IIUniversidad de SevillaSevillaSpain

Bibliographic information