2 citations · 5 across the 7 of their papers we have counts for
9 papers
Shock waves of spherical/cylindrical KdV-B: Asymptotic, stability, superposition
Alexey Samokhin
Spherical and cylindrical KdV-B equations have few known exact solutions, yet these solutions are hard to be interpreted physically. But these equations do have a family of divergi…
Superposition of shock waves of the generalized BBM equation
Alexey Samokhin
The generalized BBM studied in this paper contains an additional dissipative term. Thus instead of solitons for the classic BBM there exists a lot of travelling shock wave solution…
On perturbations retaining conservation laws of difftrential equations
Alexey Samokhin
The paper deals with perturbations of the equation that have a number of conservation laws. When a small term is added to the equation its conserved quantities usually decay at ind…
On periodic boundary solutions for cylindrical and spherical KdV-Burgers equations
Alexey Samokhin
For the KdV-Burgers equations for cylindrical and spherical waves the development of a regular profile starting from an equilibrium under a periodic perturbation at the boundary is…
On connection between the splitting parameters of KdV initial datum and its conservation quantities
Alexey Samokhin
An arbitrary compact-support initial datum for the Korteweg-de Vries equation asymptotically splits into solitons and a radiation tail, moving in opposite direction. We give asimpl…
The KdV soliton crosses a dissipative and dispersive border
Alexey Samokhin
We demonstrate the behavior of the soliton which, while moving in non-dissipative and dispersion-constant medium encounters a finite-width barrier with varying dissipation and/or d…