Published in Mathematical Notes
Abstract The relation \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$xy-yx=h(y)$$\end{document}, where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{w...
Published in Mathematical Notes
Published in Mathematical Notes
Abstract The Moutard transformation for the solutions of the Davey–Stewartson II equation is constructed. It is geometrically interpreted using the spinor (Weierstrass) representation of surfaces in four-dimensional Euclidean space. Examples of solutions that have smooth fast decaying initial data and lose regularity in finite time are constructed ...
Published in Mathematical Notes
Abstract The variational problem of minimizing the energy functional that results in a second- order nonlinear differential equation of pendulum type on a finite interval with natural boundary conditions is analyzed. It is shown that the number of solutions of the boundary-value problem depends on the length \documentclass[12pt]{minimal} \usepackag...
Published in Mathematical Notes
Abstract The paper deals with the study of time-periodic solutions of boundary layer type for a two-dimensional reaction-diffusion problem with a small parameter at the parabolic operator in the case of singularly perturbed boundary conditions of the second kind. The asymptotic approximation with respect to the small parameter for solutions with a ...
Published in Mathematical Notes
Abstract In this paper, we apply the asymptotic method developed by V. P. Maslov [1] to obtain the approximated shock-type solutions of the generalized Riemann problem (GRP) to the Buckley–Leverett equation. We calculate the the Hugoniot–Maslov chain (an infinite ODE system) whose fulfillment is a necessary condition that must be satisfied by the c...
Published in Mathematical Notes
Published in Mathematical Notes
Published in Mathematical Notes
Abstract The question of the representability of a continuous function on \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb R^d$$\end{document} in the form of the...
Published in Mathematical Notes
Abstract Criteria for the flexibility, rigidity, and almost rigidity of nonnormal affine toric varieties are obtained. For rigid and almost rigid toric varieties, automorphism groups are explicitly calculated.
