Gasdynamic regularity: some classifying geometrical remarks.
Generalizations of Melin's inequality to systems
We discuss a recent necessary and sufficient condition for Melin's inequality for a class of systems of pseudodifferential operators.
Generalized Hasimoto transform of one-dimensional dispersive flows into compact Riemann surfaces.
Generalized solutions by Cauchy's method of characteristics
Geodesic flow on SO(4), Kac-Moody Lie algebra and singularities in the complex t-plane.
The article studies geometrically the Euler-Arnold equations associatedto geodesic flow on SO(4) for a left invariant diagonal metric. Such metric were first introduced by Manakov [17] and extensively studied by Mishchenko-Fomenko [18] and Dikii [6]. An essential contribution into the integrability of this problem was also made by Adler-van Moerbeke [4] and Haine [8]. In this problem there are four invariants of the motion defining in C4 = Lie(SO(4) ⊗ C) an affine Abelian surface as complete intersection...
Geometry of KDV (1): Addition and the unimodular spectral classes.
This is the first of three papers on the geometry of KDV. It presents what purports to be a foliation of an extensive function space into which all known invariant manifolds of KDV fit naturally as special leaves. The two main themes are addition (each leaf has its private one) and unimodal spectral classes (each leaf has a spectral interpretation).
Geometry of the Complex Homogeneous Monge-Ampère Equation.
Global behaviour and symmetry properties of singular solutions of nonlinear elliptic equations
Ground states of semilinear elliptic equations : a geometric approach
Group classification of the general evolution equation: local and quasilocal symmetries.
Group Classification of Variable Coefficient Quasilinear Reaction-diffusion Equations