Nonlinear Systems and Their Remarkable Mathematical Structures, Volume II 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.
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.