W. Krawcewicz

activity

20152025

most citedExistence and Spatio-Temporal Patterns of Periodic Solutions to Second Order Non-Autonomous Equivariant Delayed Systems

3 citations · 6 across the 15 of their papers we have counts for

collaborators

17 papers

math.AP2025

Global Bifurcation of Spiral Wave Solutions to the Complex Ginzburg-Landau Equation

Carlos Garcia-Azpeitia, Ziad Ghanem, Wieslaw Krawcewicz

We use the $T^{2}$ -equivariant degree to establish the existence of unbounded branches of rotating spiral wave solutions with any number of arms for the complex Ginzburg Land…

math.AP2025

Global Bifurcation In Four-Component Bose-Einstein Condensates In Space

Carlos García-Azpeitia, Anna Gołȩbiewska, Wieslaw Krawcewicz +1

We analyze a system of coupled Bose-Einstein condensates in the domain of a unitary ball in $R^{3}$ . The coupling is due to atom-to-atom interactions that occur between diff…

math.AP2024

Global Bifurcation in Symmetric Systems of Nonlinear Wave Equations

Carlos Garcia-Azpeitia, Ziad Ghanem, Wieslaw Krawcewicz

In this paper, we use the equivariant degree theory to establish a global bifurcation result for the existence of non-stationary branches of solutions to a nonlinear, two-parameter…

math.DS2023

Equivariant Global Hopf Bifurcation in Abstract Nonlinear Parabolic Equations

Zalman Balanov, Wieslaw Krawcewicz, Arnaja Mitra +1

In this paper we study local and global symmetric Hopf bifurcation in abstract parabolic systems by means of the twisted equivariant degree.

math.DS2020

Subharmonic Solutions In Reversible Non-Autonomous Differential Equations

Izuchukwu Eze, Carlos Garcia-Azpeitia, Wieslaw Krawcewicz +1

We study the existence of subharmonic solutions in the system $u ¨ (t) = f (t, u (t))$ , where $u (t) \in R^{k}$ and $f$ is an even and $p$ -periodic function in time. Under so…

math.DS2020

Periodic Solutions to Reversible Second Order Autonomous DDEs in Prescribed Symmetric Nonconvex Domains

Zalman Balanov, Norimichi Hirano, Wieslaw Krawcewicz +2

The existence and spatio-temporal patterns of $2 π$ -periodic solutions to second order reversible equivariant autonomous systems with commensurate delays are studied using the Brouw…

math.DS2020★ 1 cited

Periodic Solutions to Reversible Second Order Autonomous Systems with Commensurate Delays

Zalman Balanov, Fulai Chen, Jing Guo +1

Existence and spatio-temporal patterns of periodic solutions to second order reversible equivariant autonomous systems with commensurate delays are studied using the Brouwer $O(2)…

math.DS2020★ 3 cited

Existence and Spatio-Temporal Patterns of Periodic Solutions to Second Order Non-Autonomous Equivariant Delayed Systems

Zalman Balanov, Wieslaw Krawcewicz, Norimichi Hirano +1

Existence and spatio-temporal symmetric patterns of periodic solutions to second order reversible equivariant non-autonomous periodic systems with multiple delays are studied under…

math.AP2020

Patterns of Non-Radial Solutions to Coupled Semilinear Elliptic Systems on a Disc

Z. Balanov, E. Hooton, W. Krawcewicz +1

In this paper, we prove the existence of non-radial solutions to the problem $- △ u = f (z, u)$ , $u ∣_{\partial D} = 0$ on the unit disc $D := {z \in C : ∣ z ∣ < 1}$ with $u(z)\…

math.DS2018

Solutions of Fixed Period in the Nonlinear Wave Equation on Networks

Carlos García-Azpeitia, Wieslaw Krawcewicz, Yanli Lv

The wave equation on network is defined by $\partial_{tt} u = Δ_{G} u + g (u)$ , where $u \in R^{n}$ and the graph Laplacian $Δ_{G}$ is an operator on functions on $n$ vertices. We…

math.DS2018

Nonlinear Vibrations in the Fullerene Molecule $C_{60}$

Carlos García-Azpeitia, Wieslaw Krawcewicz, Manuel Tejada-Wriedt +1

In this paper we analyze nonlinear dynamics of the fullerene molecule. We prove the existence of global branches of periodic solutions emerging from an icosahedral equilibrium (non…

math.DS2017

Symmetries of Nonlinear Vibrations in Tetrahedral Molecular Configurations

Irina Berezovik, Carlos García-Azpeitia, Wieslaw Krawcewicz

We study nonlinear vibrational modes of oscillations for tetrahedral configurations of particles. In the case of tetraphosphorus, the interaction of atoms is given by bond stretchi…

math.DS2017★ 1 cited

Hopf Bifurcation of Relative Periodic Solutions: Case Study of a Ring of Passively Mode-Locked Lasers

Zalman Balanov, Pavel Kravetc, Wieslaw Krawcewicz +1

In this paper, we consider an equivariant Hopf bifurcation of relative periodic solutions from relative equilibria in systems of functional differential equations respecting $Γ\tim…

math.DS2017

Dihedral Molecular Configurations Interacting by Lennard-Jones and Coulomb Forces

Irina Berezovik, Qingwen Hu, Wieslaw Krawcewicz

In this paper, we investigate periodic vibrations of a group of particles with a dihedral configuration in the plane governed by the Lennard-Jones and Coulomb forces. Using the gra…

math.DS2016

Multiple Periodic Solutions for $Γ$ -symmetric Newtonian Systems

Mieczyslaw Dabkowski, Wieslaw Krawcewicz, Yanli Lv +1

The existence of periodic solutions in $Γ$ -symmetric Newtonian systems $x ¨ = - \nabla f (x)$ can be effectively studied by means of the $(Γ \times O (2))$ -equivariant gradient degr…

math.OC2016

Non-invasive stabilization of periodic orbits in $O_{4}$ -symmetrically coupled Van der Pol oscillators

Zalman Balanov, Edward Hooton, Wieslaw Krawcewicz +1

Pyragas time delayed feedback control has proven itself as an effective tool to non-invasively stabilize periodic solutions. In a number of publications, this method was adapted to…

math.DS2015★ 1 cited

Sliding Hopf bifurcation in interval systems

E. Hooton, Z. Balanov, W. Krawcewicz +1

In this paper, the equivariant degree theory is used to analyze the occurrence of the Hopf bifurcation under effectively verifiable mild conditions. We combine the abstract result…