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The book aims to describe some recent progress in nonlinear differential equations and nonlinear dynamical systems (both continuous and discrete).
Nonlinear Systems and Their Remarkable Mathematical Structures
Part A: Nonlinear Integrable Systems
A1. Systems of nonlinearly-coupled differential equations solvable
F Calogero
A2. Integrable nonlinear PDEs on the half-line
A S Fokas and B Pelloni
A3. Detecting discrete integrability: the singularity approach
Grammaticos, A Ramani, R Willox and T Mase
A4. Elementary introduction to discrete soliton equations J Hietarinta
A5. New results on integrability of the Kahan-Hirota-Kimura discretizations
Yu B Suris and M Petrera
Part B: Solution Methods and Solution Structures
B1. Dynamical systems satisfied by special polynomials and related isospectral matrices defined in terms of their zeros
O Bihun
B2. Singularity methods for meromorphic solutions of differential equations
R Conte, T W Ng and C Wu
B3. Pfeiffer-Sato solutions of Buhl's problem and a Lagrange-D'Alembert principle for Heavenly equations
O E Hentosh, Ya A Prykarpatsky, D Blackmore and A Prykarpatski
B4. Superposition formulae for nonlinear integrable equations in bilinear form
X B Hu
B5. Matrix solutions for equations of the AKNS system
C Schiebold
B6. Algebraic traveling waves for the generalized KdV-Burgers equation and the Kuramoto-Sivashinsky equation
C Valls
Part C: Symmetry Methods for Nonlinear Systems
C1. Nonlocal invariance of the multipotentialisations of the Kupershmidt equation and its higher-order hierarchies
M Euler and N Euler
C2. Geometry of normal forms for dynamical systems
G Gaeta
C3. Computing symmetries and recursion operators of evolutionary super-systems using the SsTools environment
A V Kiselev, A O Krutov and T Wolf
C4. Symmetries of It^o stochastic differential equations and their applications R Kozlov
C5. Statistical symmetries of turbulence
M Oberlack, M Wac lawczyk and V Grebenev
Part D: Nonlinear Systems in Applications
D1. Integral transforms and ordinary differential equations of infinite order
A Chavez, H Prado and E G Reyes
D2. The role of nonlinearity in geostrophic ocean flows on a sphere
A Constantin and R S Johnson
D3. Review of results on a system of type many predators - one prey
A V Osipov and G S oderbacka
D4. Ermakov-type systems in nonlinear physics and continuum mechanics
C Rogers and W K Schief