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2013
Impact Factor

Dmitry Sinelshchikov

Kashirskoe sh. 31, Moscow 115409, Russia
Moscow Engineering and Physics Institute

Publications:

Garashchuk I. R., Sinelshchikov D. I., Kudryashov N. A.
Nonlinear Dynamics of a Bubble Contrast Agent Oscillating near an Elastic Wall
2018, vol. 23, no. 3, pp.  257-272
Abstract
Contrast agent microbubbles, which are encapsulated gas bubbles, are widely used to enhance ultrasound imaging. There are also several new promising applications of the contrast agents such as targeted drug delivery and noninvasive therapy. Here we study three models of the microbubble dynamics: a nonencapsulated bubble oscillating close to an elastic wall, a simple coated bubble and a coated bubble near an elastic wall.We demonstrate that complex dynamics can occur in these models. We are particularly interested in the multistability phenomenon of bubble dynamics. We show that coexisting attractors appear in all of these models, but for higher acoustic pressures for the models of an encapsulated bubble.We demonstrate how several tools can be used to localize the coexisting attractors. We provide some considerations why the multistability can be undesirable for applications.
Keywords: contrast agent, dynamical system, nonlinear dynamics, dynamical chaos, multistability, coexisting attractors
Citation: Garashchuk I. R., Sinelshchikov D. I., Kudryashov N. A.,  Nonlinear Dynamics of a Bubble Contrast Agent Oscillating near an Elastic Wall, Regular and Chaotic Dynamics, 2018, vol. 23, no. 3, pp. 257-272
DOI:10.1134/S1560354718030036
Kudryashov N. A., Sinelshchikov D. I.
On the Connection of the Quadratic Lienard Equation with an Equation for the Elliptic Functions
2015, vol. 20, no. 4, pp.  486-496
Abstract
The quadratic Lienard equation is widely used in many applications. A connection between this equation and a linear second-order differential equation has been discussed. Here we show that the whole family of quadratic Lienard equations can be transformed into an equation for the elliptic functions. We demonstrate that this connection can be useful for finding explicit forms of general solutions of the quadratic Lienard equation. We provide several examples of application of our approach.
Keywords: quadratic lienard equation, elliptic functions, nonlocal transformations, general solution
Citation: Kudryashov N. A., Sinelshchikov D. I.,  On the Connection of the Quadratic Lienard Equation with an Equation for the Elliptic Functions, Regular and Chaotic Dynamics, 2015, vol. 20, no. 4, pp. 486-496
DOI:10.1134/S1560354715040073
Kudryashov N. A., Sinelshchikov D. I.
Special Solutions of a High-order Equation for Waves in a Liquid with Gas Bubbles
2014, vol. 19, no. 5, pp.  576-585
Abstract
A fifth-order nonlinear partial differential equation for the description of nonlinear waves in a liquid with gas bubbles is considered. Special solutions of this equation are studied. Some elliptic and simple periodic traveling wave solutions are constructed. Connection of selfsimilar solutions with Painlevé transcendents and their high-order analogs is discussed.
Keywords: waves in a liquid with gas bubbles, evolution equations, exact solutions, meromorphic solutions, fifth-order KdV equation, Kaup–Kupershmidt equation
Citation: Kudryashov N. A., Sinelshchikov D. I.,  Special Solutions of a High-order Equation for Waves in a Liquid with Gas Bubbles, Regular and Chaotic Dynamics, 2014, vol. 19, no. 5, pp. 576-585
DOI:10.1134/S1560354714050050

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