Most nonlinear differential equations arising in natural sciences admit chaotic behaviour and
cannot be solved analytically. Integrable systems lie on the other extreme. They possess …

Differential equations, especially nonlinear, present the most effective way for describing
complex physical processes. Methods for constructing exact solutions of differential …

The Whitham modulation equations for the defocusing nonlinear Schrödinger (NLS)
equation in two, three and higher spatial dimensions are derived using a two-phase ansatz …

HyperCR Einstein–Weyl equations in 2+ 1 dimensions reduce to a pair of quasi-linear PDEs
of hydrodynamic type. All solutions to this hydrodynamic system can in principle be …

Recently, a hydrodynamic description of local equilibrium dynamics in quantum integrable
systems was discovered. In the diffusionless limit, this is equivalent to a certain'Bethe …

arXiv:nlin/0312043v1 [nlin.SI] 19 Dec 2003 Hydrodynamic reductions and solutions of a
universal hierarchy Page 1 arXiv:nlin/0312043v1 [nlin.SI] 19 Dec 2003 Hydrodynamic …

For several classes of second-order dispersionless PDEs, we show that the symbols of their
formal linearizations define conformal structures that must be Einstein-Weyl in 3D (or self …

We introduce and study a new class of kinetic equations, which arise in the description of
nonequilibrium macroscopic dynamics of soliton gases with elastic collisions between …

The equations governing anti-self-dual and Einstein-Weyl conformal geometries can be
regarded as “master dispersionless systems” in four and three dimensions, respectively …

Let u be a function of n independent variables x1,…, xn, and let U=(uij) be the Hessian
matrix of u. The symplectic Monge–Ampère equation is defined as a linear relation among …