arXiv subjects

S. Dobrokhotov

Publications and source records attributed to S. Dobrokhotov.

3 recordsLinked to original sources

arXiv2014

On applications of Maupertuis-Jacobi correspondence for Hamiltonians $F(x,|p|)$ in some 2-D stationary semiclassical problems

We make use of the Maupertuis -- Jacobi correspondence, well known in Classical Mechanics, to simplify 2-D asymptotic formulas based on Maslov's canonical operator, when constructing Lagrangian manifolds invariant with respect to phase flows for Hamiltonians of the form $F(x,|p|)$. As examples we consider Hamiltonians coming from the Schrödinger equation, the 2-D Dirac equation for graphene and linear water wave theory.

math-ph↗

arXiv2012

Functions of noncommuting operators in an asymptotic problem for a 2D wave equation with variable velocity and localized right-hand side

We use the theory of functions of noncommuting operators (noncommutative analysis) to solve an asymptotic problem for a partial differential equation and show how, starting from general constructions and operator formulas that seem to be rather abstract from the viewpoint of differential equations, one can end up with very specific, easy-to-evaluate expressions for the solution, useful, e.g., in the tsunami wave problem.

math.AP↗

arXiv2004

On Maslov Conjecture about Square Root Type Singular Solutions of the Shallow Water Equations

We prove Maslov's conjecture that the structure of the type of square root of a quadratic form is the unique structure of weakly singular solutions (with a point singularity) of the shallow water equations with the properties of asymptotic self-similarity and stability. This fact plays a key role in the study of the dynamics of vortical singularities and their applications to the description of typhoon trajectories.

math-ph↗