106 citations · 722 across the 27 of their papers we have counts for
27 papers
Bubbling transition as a mechanism of destruction of synchronous oscillations of identical microbubble contrast agents
Ivan Garashchuk, Dmitry Sinelshchikov
We study the process of destruction of synchronous oscillations in a model of two interacting microbubble contrast agents exposed to an external ultrasound field. Completely synchr…
On linearizability via nonlocal transformations and first integrals for second-order ordinary differential equations
Dmitry Sinelshchikov
Nonlinear second-order ordinary differential equations are common in various fields of science, such as physics, mechanics and biology. Here we provide a new family of integrable s…
Synchronous oscillations and symmetry breaking in a model of two interacting ultrasound contrast agents
Ivan R. Garashchuk, Alexey O. Kazakov, Dmitry I. Sinelshchikov
We study nonlinear dynamics in a system of two coupled oscillators, describing the motion of two interacting microbubble contrast agents. In the case of identical bubbles, the corr…
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…
Extended two dimensional equation for the description of nonlinear waves in gas-liquid mixture
Nikolay A. Kudryashov, Dmitry I. Sinelshchikov, Alexander K. Volkov
We consider a system of equations for the description of nonlinear waves in a liquid with gas bubbles. Taking into account high order terms with respect to a small parameter, we de…