Soliton and caviton solutions for the non-local Whitham equation
About current research
In the framework of cooperation with the head of state department of the Institute of physical chemistry and electrochemistry of RAS A. M. Malkin and Professor of the Moscow aviation Institute N.E. Kulagin studiedsoliton and caviton solutions (soliton solutions with exacerbations) for non-localthe Whitham equation, which simulates, in particular, the propagation of compression waves of a compressibleliquids in thin tubes.
The main types of such solutions in various fields are studiedchanges to the equation parameters. This solutions correspond to homoclinic smooth and non-smooth solutions for equilibrium states of types saddle-center and saddle-focus respectively.
Two articles have been prepared for publication in "Phys. Rev Letters" and "Communications in Nonlinear Science and Numerical Simulations".