Nonlinear Systems and Their Remarkable Mathematical Structures

The book aims to describe some recent progress in nonlinear differential equations and nonlinear dynamical systems (both continuous and discrete).

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