Nonlinear Systems and Their Remarkable Mathematical Structures. Volume II
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 theo...
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| Format: | eBook |
| Language: | English |
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Milton :
CRC Press LLC,
2019.
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| Online Access: | Connect to the full text of this electronic book |
Table of Contents:
- Cover; Half Title; Title Page; Copyright Page; Table of Contents; Preface; The Authors; Part A: Integrability, Lax Pairs and Symmetry; A1. Reciprocal transformations and their role in the integrability and classification of PDEs; 1. Introduction; 2. Fundamentals; 3. Reciprocal transformations as a way to identify and classify PDEs; 4. Reciprocal transformations to derive Lax pairs; 5. A Miura-reciprocal transformation; 6. Conclusions; A2. Contact Lax pairs and associated (3+1)-dimensional integrable dispersionless systems; 1. Introduction; 2. Isospectral versus nonisospectral Lax pairs
- A4. Lie point symmetries of delay ordinary differential equations1. Introduction; 2. Illustrating example; 3. Formulation of the problem for first-order DODEs; 4. Construction of invariant first-order DODSs; 5. First-order linear DODSs; 6. Lie symmetry classification of first-order nonlinear DODSs; 7. Exact solutions of the DODSs; 8. Higher order DODSs; 9. Traffic flow micro-model equation; 10. Conclusions; A5. The symmetry approach to integrability: recent advances; 1. Introduction; 2. The symmetry approach to integrability; 3. Integrable non-abelian equations; 4. Non-evolutionary systems