3 papers
math-ph2001
Exact self-similar and two-phase solutions of systems of semilinear parabolic equations
K. A. Volosov, V. G. Danilov, A. M. Loginov
Exact single-wave and two-wave solutions of systems of equations of Newell-Whitehead type are presented. The Painleve test and calculations in the spirit of Hirota are used to cons…
math-ph2000
Propagation and interaction of shock waves of quasilinear equation
Vladimir G. Danilov, Vladimir M. Shelkovich
We propose a new regularization method for constructing a shock wave type solution with nonsmooth front (interaction of shock waves) for quasilinear equations in the one-dimensiona…
math-ph2000
Propagation of infinitely narrow delta-solitons
Vladimir G. Danilov, Vladimir M. Shelkovich
We construct a definition of the weak solution to KdV type equations with small dispersion admitting the zero dispersion limit for soliton-like solutions. Using this definition, we…