Nonlinear Systems and Their Remarkable Mathematical Structures, Volume 2 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.


  • 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

part A|205 pages

Integrability, Lax Pairs and Symmetry

chapter A1|28 pages

Reciprocal transformations and their role in the integrability and classification of PDEs

ByP. Albares, P.G. Estévez, C. Sardón

chapter A2|30 pages

Contact Lax pairs and associated (3+1)-dimensional integrable dispersionless systems

ByMaciej Błaszak, Artur Sergyeyev

chapter A3|30 pages

Lax pairs for edge-constrained Boussinesq systems of partial difference equations

ByTerry J. Bridgman, Willy Hereman

chapter A4|30 pages

Lie point symmetries of delay ordinary differential equations

ByVladimir A. Dorodnitsyn, Roman Kozlov, Sergey V. Meleshko, Pavel Winternitz

chapter A5|39 pages

The symmetry approach to integrability: recent advances

ByRafael Hernández Heredero, Vladimir Sokolov

chapter A6|30 pages

Evolution of the concept of λ–symmetry and main applications

ByC. Muriel, J.L. Romero

part B|239 pages

Algebraic and Geometric Methods

chapter B1|43 pages

Coupled nonlinear Schrödinger equations: spectra and instabilities of plane waves

ByAntonio Degasperis, Sara Lombardo, Matteo Sommacal

chapter B2|45 pages

Rational solutions of Painlevé systems.

ByDavid Gómez-Ullate, Yves Grandati, Robert Milson

chapter B3|32 pages

Cluster algebras and discrete integrability

ByAndrew N.W. Hone, Philipp Lampe, Theodoros E. Kouloukas

chapter B4|30 pages

A review of elliptic difference Painlevé equations

ByNalini Joshi, Nobutaka Nakazono

chapter B5|26 pages

Linkage mechanisms governed by integrable deformations of discrete space curves

ByShizuo Kaji, Kenji Kajiwara, Hyeongki Park

chapter B6|33 pages

The Cauchy problem of the Kadomtsev-Petviashvili hierarchy and infinite-dimensional groups

ByJean-Pierre Magnot, Enrique G. Reyes

chapter B7|30 pages

Wronskian solutions of integrable systems

ByDa-jun Zhang

part C|82 pages