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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

2. Cluster algebras: definition and examples

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. Features 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

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