55 citations · 89 across the 12 of their papers we have counts for
14 papers
The limit cycles in a generalized Rayleigh-Liénard oscillator
Lubomir Gavrilov, Iliya D. Iliev
We compute the cyclicity of open period annuli of the following generalized Rayleigh-Liénard equation $$\ddot{x}+ax+bx^3-(λ_1+λ_2 x^2+λ_3\dot{x}^2+λ_4 x^4+λ_5\dot{x}^4+λ_6 x^6)\dot…
Recursion operators and the hierarchies of MKdV equations related to , and Kac-Moody algebras
V. S. Gerdjikov, A. A. Stefanov, I. D. Iliev +4
We constructed the three nonequivalent gradings in the algebra . The first one is the standard one obtained with the Coxeter automorphism $C_1=S_{α_2} S_{α_1}S_{α…
On the cubic perturbations of the symmetric 8-loop Hamiltonian
Iliya D. Iliev, Chengzhi Li, Jiang Yu
We study arbitrary cubic perturbations of the symmetric 8-loop Hamiltonian, which are linear with respect to the small parameter. It is shown that when the first 4 coefficients in…
Cubic perturbations of elliptic Hamiltonian vector fields of degree three
Lubomir Gavrilov, Iliya D. Iliev
The purpose of the present paper is to study the limit cycles of one-parameter perturbed plane Hamiltonian vector field $$ X_\varepsilon : \left\{ \begin{array}{llr…
Perturbations of quadratic Hamiltonian two-saddle cycles
Lubomir Gavrilov, Iliya D. Iliev
We prove that the number of limit cycles, which bifurcate from a two-saddle loop of a planar quadratic Hamiltonian system, under an arbitrary quadratic deformation, is less than or…
Stability of periodic traveling waves for the quadratic and cubic nonlinear Schrödinger equations
Sevdzhan Hakkaev, Iliya D. Iliev, Kiril Kirchev
We study the existence and stability of periodic traveling-wave solutions for the quadratic and cubic nonlinear Schrödinger equations in one space dimension.