106 citations · 722 across the 27 of their papers we have counts for
12 papers · 1 filter
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…
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…
On the integrability conditions for a family of the Liénard-type equations
Nikolai A. Kudryashov, Dmitry I. Sinelshchikov
We study a family of Liénard--type equations. Such equations are used for the description of various processes in physics, mechanics and biology and also appear as traveling--wave…
New non-standard Lagrangians for the Liénard-type equations
Nikolai A. Kudryashov, Dmitry I. Sinelshchikov
Liénard-type equations are used for the description of various phenomena in physics and other fields of science. Here we find a new family of the Liénard-type equations which admit…
On the criteria for integrability of the Liénard equation
Nikolai A. Kudryashov, Dmitry I. Sinelshchikov
The Liénard equation is of a high importance from both mathematical and physical points of view. However a question about integrability of this equation has not been completely ans…
Analytical solutions for problems of bubble dynamics
Nikolai A. Kudryashov, Dmitry I. Sinelshchikov
Recently, an asymptotic solution of the Rayleigh equation for an empty bubble in dimensions has been obtained. Here we give the closed--from general analytical solution of this…