Nonlinear Systems and Their Remarkable Mathematical Structures: Volume 1 [Hardcover]

Part A: Nonlinear Integrable Systems A1. Systems of nonlinearly-coupled differential equations solvable A2. Integrable nonlinear PDEs on the half-line A3. Detecting discrete integrability: the singularity approach A4. Elementary introduction to discrete soliton equations A5. New results on integrability of the Kahan-Hirota-Kimura discretizations Part B: Solution Methods and Solution Structures B1. Dynamical systems satisfied by special polynomials and related isospectral matrices defined in terms of their zeros B2. Singularity methods for meromorphic solutions of differential equations B3. Pfeiffer-Sato solutions of Buhl's problem and a Lagrange-D'Alembert principle for Heavenly equations B4. Superposition formulae for nonlinear integrable equations in bilinear form B5. Matrix solutions for equations of the AKNS system B6. Algebraic traveling waves for the generalized KdV-Burgers equation and the Kuramoto-Sivashinsky equation Part C: Symmetry Methods for Nonlinear Systems C1. Nonlocal invariance of the multipotentialisations of the Kupershmidt equation and its higher-order hierarchies C2. Geometry of normal forms for dynamical systems C3. Computing symmetries and recursion operators of evolutionary super-systems using the SsTools environment C4. Symmetries of It^o stochastic differential equations and their applications C5. Statistical symmetries of turbulence Part D: Nonlinear Systems in Applications D1. Integral transforms and ordinary differential equations of infinite order D2. The role of nonlinearity in geostrophic ocean flows on a sphere D3. Review of results on a system of type many predators - one prey D4. Ermakov-type systems in nonlinear physics and continuum mechanics

 

The book aims to describe some recent progress in nonlinear differential equationslÃ4