765 citations · 1.3k across the 24 of their papers we have counts for
24 papers
Closed-form solutions of the nonlinear Schrödinger equation with arbitrary dispersion and potential
Andrei D. Polyanin, Nikolay A. Kudryashov
For the first time, the general nonlinear Schrödinger equation is investigated, in which the chromatic dispersion and potential are specified by two arbitrary functions. The equati…
Lax representation and quadratic first integrals for a family of non-autonomous second-order differential equations
Dmitry I. Sinelshchikov, Ilia Yu. Gaiur, Nikolay A. Kudryashov
We consider a family of non-autonomous second-order differential equations, which generalizes the Liénard equation. We explicitly find the necessary and sufficient conditions for m…
Hyperchaos and Multistability in Nonlinear Dynamics of Two Interacting Microbubble Contrast Agents
Ivan R. Garashchuk, Dmitry I. Sinelshchikov, Alexey O. Kazakov +1
We study nonlinear dynamics of two coupled contrast agents that are micro-meter size gas bubbles encapsulated into a viscoelastic shell. Such bubbles are used for enhancing ultraso…
On connections of the Liénard equation with some equations of Painlevé--Gambier type
Nikolay Kudryashov, Dmitry Sinelshchikov
The Liénard equation is used in various applications. Therefore, constructing general analytical solutions of this equation is an important problem. Here we study connections betwe…
Integrable model of nonlinear dislocations
Nikolay A Kudryashov
Using the continuous limit approximation in the dynamical system we study a nonlinear partial differential equation which corresponds to the generalization of both the Fermi-Pasta-…
Metal hydrogen critical temperature at the pressure 500 GPa
Nikolay Kudryashov, Alexander Kutukov, Evgeny Mazur
Éliashberg theory, being generalized to the case of the electron-phonon (EP) systems with the not constant density of electronic states, as well as to the frequency behavior of the…