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Conservation laws vanishing along characteristic directions of a given system of PDEs are known as characteristic conservation laws, or characteristic integrals. In 2D, they play an important role in the theory of Darboux-integrable equations. In this paper we discuss characteristic integrals in 3D and demonstrate that, for a class of second-order linearly degenerate dispersionless integrable PDEs, the corresponding characteristic integrals are parametrised by points on the Veronese variety.
We investigate second order quasilinear equations of the form f_{ij} u_{x_ix_j}=0 where u is a function of n independent variables x_1, ..., x_n, and the coefficients f_{ij} are functions of the first order derivatives p^1=u_{x_1}, >..., p^n=u_{x_n}
The Moutard transformation for a two-dimensional Dirac operator with a complex-valued potential is constructed. It is showed that this transformation relates the potentials of Weierstrass representations of surfaces related by a composition of the in
These notes were inspired by the course Quantum Field Theory from a Functional Integral Point of View given at the University of Zurich in Spring 2017 by Santosh Kandel. We describe Feynmans path integral approach to quantum mechanics and quantum fie
Based on the well-established theory of discrete conjugate nets in discrete differential geometry, we propose and examine discrete analogues of important objects and notions in the theory of semi-Hamiltonian systems of hydrodynamic type. In particula
We introduce a useful and rather simple classes of BKP tau functions which which we shall shall call easy tau functions. We consider the large BKP hiearchy related to $O(2infty +1)$ which was introduced in cite{KvdLbispec} (which is closely related t