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 …

Analogues of the KP and the Toda lattice hierarchy called dispersionless KP and Toda
hierarchy are studied. Dressing operations in the dispersionless hierarchies are introduced …

The Handbook of Nonlinear Partial Differential Equations is the latest in a series of
acclaimed handbooks by these authors and presents exact solutions of more than 1600 …

John Hornstein has written about the author's theorem on nonintegrability of geodesic flows
on closed surfaces of genus greater than one:" Here is an example of how differential …

In this study, we delve into the exploration of the (2+ 1)-dimensional potential Kadomtsev-
Petviashvili (pKP) and Calogero–Degasperis equation (CDE) models, which hold significant …

We show that conformal maps of simply connected domains with an analytic boundary to a
unit disk have an intimate relation to the dispersionless 2D Toda integrable hierarchy. The …

Abstract A (2+ 1)-dimensional quasilinear system is said to be 'integrable'if it can be
decoupled in infinitely many ways into a pair of compatible n-component one-dimensional …

Книга содержит точные решения около 1200 нелинейных уравнений математической
физики и механики. Рассматриваются уравнения параболического, гиперболического …

We give an algebraic method to construct an infinite number of exact solutions of the KP
hierarchy in terms of the hodograph transform. These solutions are obtained from a unique …

It is shown that Einstein–Weyl (EW) equations in 2+ 1 dimensions contain the dispersionless
Kadomtsev–Petviashvili (dKP) equation as a special case: if an EW structure admits a …