4 citations · 6 across the 4 of their papers we have counts for
4 papers
Application of invariants of characteristics to construction of solutions without gradient catastrophe
Alexander V. Aksenov, Konstantin P. Druzhkov, Oleg V. Kaptsov
The one-dimensional system of equations of isentropic gas dynamics is considered. First-order invariants of characteristics of this system are classified. Second-order invariants o…
On the correspondence between variational principles in Eulerian and Lagrangian descriptions
Alexander V. Aksenov, Konstantin P. Druzhkov
A relation between variational principles for equations of continuum mechanics in Eulerian and Lagrangian descriptions is considered. It is shown that for a system of differential…
Construction of complex solutions to nonlinear partial differential equations using simpler solutions
Alexander V. Aksenov, Andrei D. Polyanin
The paper describes a number of simple but quite effective methods for constructing exact solutions of PDEs, that involve a relatively small amount of intermediate calculations. Th…
Conservation laws of the system of equations of one-dimensional shallow water over uneven bottom in Lagrange's variables
Alexander V. Aksenov, Konstantin P. Druzhkov
The system of equations of one-dimensional shallow water over uneven bottom in Euler's and Lagrange's variables is considered. Intermediate system of equations is introduced. Hydro…