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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