Complete classification of stationary flows with constant total pressure of ideal incompressible infinitely conducting fluid

The exhaustive classification of stationary incompressible flows with constant total pressure of ideal infinitely electrically conducting fluid is given. By introduction of curvilinear coordinates based on streamlines and magnetic lines of the flow the system of magnetohydrodynamics (MHD) equations is reduced to a nonlinear vector wave equation extended by the incompressibility condition in a form of a generalized Cauchy integral. For flows with constant total pressure the wave equation is explicitly integrated, whereas the incompressibility condition is reduced to a scalar equation for functions, depending on different sets of variables. The central difficulty of the investigation is the separation of variables in the scalar equation, and integration of the resulting overdetermined systems of nonlinear partially differential equations. The canonical representatives of all possible types of solutions together with equivalence transformations, that extend the canonical set to the whole amount of solutions are represented

On the hierarchy of partially invariant submodels of differential equations

It is noticed, that partially invariant solution (PIS) of differential equations in many cases can be represented as an invariant reduction of some PIS of the higher rank. This introduce a hierarchic structure in the set of all PISs of a given system of differential equations. By using this structure one can significantly decrease an amount of calculations required in enumeration of all PISs for a given system of partially differential equations. An equivalence of the two-step and the direct ways of construction of PISs is proved. In this framework the complete classification of regular partially invariant solutions of ideal MHD equations is given

The Russian hospitality industry during a pandemic - crisis or breakthrough?

This article examines the most pressing problematic issues of stagnation in the hospitality industry in Russia, associated with the new challenges of the coronavirus pandemic, both at the international and national levels. The author analyzes new trends and structural changes in the industry and assesses the prospects for overcoming the difficult crisis. The article presents specific proposals aimed at the restoration and constructive development of the tourism industry both for the authorities and administration to amend the adopted Strategy for the development of tourism in the Russian Federation for the period up to 2035, and for business structures, as well as travel companies. According to the author, the hospitality industry can still face serious shocks in the near future and the industry will not come out of the crisis without experiencing repeated shocks and border closings. Nevertheless, tourism is known for its ability to withstand economic downturns and can play a key role in reviving both the global and Russian economies as they emerge from the crisis. To consolidate the trend and to strengthen the development of domestic tourism, the industry needs a coordinated position and strategies for the behavior of the main market players, such as business companies operating in the hospitality industry, as well as authorities and authorities at the federal and regional levels. This requires the development and implementation of a modern strategy, taking into account the need to overcome the crisis caused by the coronavirus pandemic, the adaptation of the strategy to new realities and sustainable development of the state at all levels