Partially Intergrable Evolution Equations in Physics

Abstract

I. Waves in Physical Systems.- Competing interactions and complexity in condensed matter.- Exact solutions of the Boltzmann equation.- Nonlinear interaction between short and long waves.- Nonlinear optics.- The phase diffusion and mean drift equations for convection at finite Rayleigh numbers in large containers I.- Nonlinear evolution equations, quasi-solitons and their experimental manifestation.- The initial-boundary value problem for the Davey-Stewartson 1 equation how to generate and drive localized coherent structures in multidimensions.- II. Instabilities and Defects.- Ginzburg-Landau models of non-equilibrium.- Nonlinear Ginzburg-Landau equation and its application to fluid-mechanics.- Defects and disorder of nonlinear waves in convection.- III. Concepts Of Integrability and Singularity Analysis.- An introduction to Kowalevski's exponents.- Singularity analysis and its relation to complete, partial and non-integrability.- A concept of integrability based on the symmetry approach.- Backlund transformations and the Painleve property.- IV. Mathematical Methods.- Differential geometry techniques for sets of nonlinear partial differential equations.- Inertial manifolds and attractors of partial differential equations.- Hirota's bilinear method and partial integrability.- Generalized symmetries, recursion operators and bihamiltonian systems.- Nonlinear dispersive equations without inverse scattering.- Group theory and exact solutions of partially integrable differential systems.- Contributed Papers.- The nonlinear evolution equation for the order parameter in superfluid Helium-Four.- Quasimonomial transformations and integrability.- Partial integrability of the damped kink equation.- New similarity reductions of Boussinesq-type equations.- The homographic invariance of PDE Painleve analysis.- The nonlocal amplitude equation.- Pressure waves in fluid-filled nonlinear viscoelastic tubes.- Elliptic function solutions for Landau-Ginzburg equation.- Application of a Macsyma program for the Painleve test to the Fitzhugh-Nagumo Equation.- The strongly dissipative Toda lattice.- A perturbative approach to Hirota's bilinear equations of KdV-type.- Construction of two dimensional super potentials for classical super systems.- Applications of nonlinear PDE's to the modelling of ferromagnetic inhomogeneities.- Author Index.