5 papers
Soliton-like solutions of the Camassa--Holm equation with variable coefficients and a small dispersion
Yuliia Samoilenko, Valerii Samoilenko
The paper deals with the Camassa--Holm equation with variable coefficients (vcCH equation) that is a direct generalization of the well known Camassa--Holm equation. We focus on the…
Asymptotic soliton-like and asymptotic peakon-like solutions of the modified Camassa-Holm equation with variable coefficients and singular perturbation
Lorenzo Brandolese, Yuliia Samoilenko, Valerii Samoilenko
The paper deals with the construction of the asymptotic soliton-like and the asymptotic peakon-like solutions to the modified Camassa-Holm equation with variable coefficicents and…
Asymptotic step-like solutions to the singularly perturbed Burgers' equation
Valerii Samoilenko, Yuliia Samoilenko, Elvira Zappale
The paper deals with a problem of asymptotic step-like solutions to the Burgers' equation with variable coefficients and a small parameter. By means of the non-linear WKB method, t…
Existence of solutions to non-homogeneous higher order differential equation in the Schwartz space
Valerii H. Samoilenko, Yuliia I. Samoilenko
There is studied problem on existence of solutions to non-homogeneous differential equation of higher even order. Similar problem arises while studying soliton and soliton-like sol…
Solvability of linear non-homogeneous higher order differential equation in the Schwartz space
Valerii Samoilenko, Yuliia Samoilenko
There is studied problem on solvability of linear non-homogeneous differential equation of higher even order. There is proved the theorem on necessary and sufficient conditions on…