In these lecture notes I consider one remarkable system of differential equations that
appeared in the papers of physicists on two-dimensional topological field theory (TFT) in the …

Exact solutions of differential equations continue to play an important role in the
understanding of many phenomena and processes throughout the natural sciences in that …

Some new similarity reductions of the Boussinesq equation, which arises in several physical
applications including shallow water waves and also is of considerable mathematical …

The Handbook of Ordinary Differential Equations: Exact Solutions, Methods, and Problems,
is an exceptional and complete reference for scientists and engineers as it contains over …

This first introductory text to discrete integrable systems introduces key notions of
integrability from the vantage point of discrete systems, also making connections with the …

In recent investigations on nonlinear dynamics, the singularity structure analysis pioneered
by Kovalevskaya, Painlevé and contempories, which stresses the meromorphic nature of the …

Many of the familiar integrable systems of equations are symmetry reductions of self-duality
equations on a metric or on a Yang-Mills connection. For example, the Korteweg-de Vries …

62 monodromy theory for the system (1.26) 80 Chapter 7. The manifold of solutions of
Painlevé II equation decreasing as I→∞. Parametrization of their asymptotics through the …

Nonlinear differential or difference equations are encountered not only in mathematics but
also in many areas of physics (evolution equations and propagation of a signal in an optical …

In this paper we discuss symmetry reductions and exact solutions of the Boussinesq
equation using the classical Lie method of infinitesimals, the direct method due to Clarkson …