Nonlinear Systems and Their Remarkable Mathematical Structures: Volume 2

ISBN-13: 9780367208479 / Angielski / Twarda / 2019 / 526 str.

Norbert Euler; Maria Clara Nucci

Opis

This book is written in a careful pedagogical manner by experts from the field of nonlinear differential equations and nonlinear dynamical systems (both continuous and discrete).

Spis treści

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.