695 citations · 1.8k across the 51 of their papers we have counts for
53 papers
Lax pair and first integrals for two of nonlinear coupled oscillators
Nikolay A. Kudryashov
The system of two nonlinear coupled oscillators is studied. As partial case this system of equation is reduced to the Duffing oscillator which has many applications for describing…
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…
The fifth-order partial differential equation for the description of the α+β Fermi-Pasta-Ulam model
Nikolay A. Kudryashov, Alexandr K. Volkov
We study a new nonlinear partial differential equation of the fifth order for the description of perturbations in the Fermi-Pasta-Ulam mass chain. This fifth-order equation is an e…
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…