Opening

• Filip Blaschke (Silesian University in Opava)

Room: Lecture hall of Institute of Mathematics

Oscillons and the zero vector problem

• Tomasz Romańczukiewicz (Jagiellonian University)

Room: Lecture hall of Institute of Mathematics

On the Solutions to the Inconsistencies in Classical Electrodynamics

• Manfried Faber (Techn. Univ. Wien)

Room: Lecture hall of Institute of Mathematics It has been known for over 100 years that there is a discrepancy between Maxwell's electrodynamics and the idea of a classical electron as the ``atom'' of electricity. This incompatibility is known under the terms 4/3 problem of the classical electron and radiation reaction force and was circumvented in the currently most successful theories, the quantum field theories, by limit value considerations, by a consistent mutual subtraction of infinities. This raises the question of what minimal changes to the fundamentals of electrodynamics should look like, which contains Maxwell's theory as a limiting case. I show that it is possible to formulate electrodynamics and stable electrons in a way that yields cross sections consistent with the results of QED. I show that it is possible to formulate electrodynamics and stable electrons without the occurrence of divergences. This description leads to electron cross sections that are consistent with the results of QED.

Shape modes of critically coupled vortices

• Nora Gavrea (University of Leeds)

Room: Lecture hall of Institute of Mathematics In this talk, I will discuss a subclass of gauged nonlinear sigma models with gauge group U(1) and a general Kaehler target. At critical coupling, such models admit topological soliton solutions called BPS vortices, which solve a system of first order PDEs called the Bogomolny equations. They attain a topological lower energy bound characterized by the degree of a holomorphic map. The most famous example is when the target is the complex plane, describing the Abelian-Higgs model. I will present a geometric formalism to compute the second variation of the energy functional around a general BPS vortex (whose existence we establish for a compact target). On a non-compact domain, such as R^2, it is a nontrivial question whether the associated Jacobi operator has any L^2 normalisable eigenfunctions. Such eigenfunctions are called shape modes, and, if present, they have a strong effect on the low energy scattering behaviour of vortices. We prove (on R^2) that all vortices have at least one shape mode, and that such shape modes can be constructed by solving a simple scalar Schroedinger PDE. This is based on joint work with Derek Harland and Martin Speight.

Multidimensional integrability revisited

• Artur Sergyeyev (Silesian University in Opava)

Room: Lecture hall of Institute of Mathematics We present novel integrable (3+1)-dimensional generalizations for the following (2+1)-dimensional integrable systems: dispersionless BKP, dispersionless asymmetric Nizhnik--Veselov--Novikov, dispersionless Gardner, and dispersionless modified KP equations, and the generalized Benney system. All these new (3+1)-dimensional integrable systems are found using our general construction for a large new class of (3+1)-dimensional integrable systems with nonisospectral Lax pairs involving contact vector fields. For further details, please see A. Sergyeyev, Multidimensional integrable systems from contact geometry. Bol. Soc. Mat. Mex. 31 (2025), art. 26, arXiv:2501.04474.

Resurgent structure of the ’t Hooft-Polyakov monopole profiles

• Michal Malinský (Charles University)

Room: Lecture hall of Institute of Mathematics

Radiation from Oscillons

• Jarah Evslin (University of Chinese Academy of Sciences)

Room: Lecture hall of Institute of Mathematics

Towards the effective field theory of cosmic strings

• Alberto Garcia Martin-Caro (Universidade de Vigo & Jagiellonian U.)

Room: Lecture hall of Institute of Mathematics To be determined

Integral Identities from Stress-Energy Conservation in Field Theory

• Leandro Roza Livramento (Instituto de Física e São Carlos, Universidade de São Paulo)

Room: Lecture hall of Institute of Mathematics We derive an infinite family of time-dependent integral relations by performing weighted integrations of the stress-energy conservation equation in classical field theory. These relations connect weighted spatial integrals of the stress tensor to the second time derivative of weighted averages of the energy density. When this quantity vanishes, as in stationary configurations, or even only at a given instant or in a time-averaged sense, the relations reduce to integral identities for weighted spatial integrals of the stress tensor, substantially extending Derrick-type virial arguments. We then obtain their explicit form for a broad class of classical bosonic field theories whose derivative terms are quadratic in spacetime tensors. Our approach provides a direct and simple way to derive these integral identities for such models. In selected cases, the resulting relations also imply bounds on temporal contributions to the total energy. The formalism is applied to study the angular frequency of compact Q-balls and Q-shells in a CPN model with a V-shaped potential and the stability of topological solitons in the Skyrme-Maxwell theory.

Nonlinear Discrete Dynamics and Stability of High-Dimensional Rational Systems

• Yacine Halim (Abdelhafid Boussouf University of Mila)

Room: Lecture hall of Institute of Mathematics We investigate the local dynamics of a class of (p)-dimensional nonlinear rational difference equation systems with power-type nonlinearities, extending several previously studied low-dimensional models to a general higher-dimensional setting. The analysis focuses on the boundedness of solutions and the local asymptotic stability of equilibrium states. By establishing explicit sufficient conditions for stability, we identify the influence of the system parameters on the qualitative behavior of trajectories near equilibria. Beyond extending existing theoretical results, the proposed framework provides a unified approach for analyzing high-dimensional discrete nonlinear systems and reveals structural features governing their local dynamics. Although the present work does not deal directly with soliton solutions, the stability techniques and dynamical analysis developed here contribute to the broader understanding of nonlinear discrete models that arise in the study of nonlinear wave propagation, lattice dynamics, and related evolution phenomena, making the results relevant to the general themes of nonlinear dynamics addressed by the workshop.

The electroweak sphaleron

• Andrzej Wereszczyński (Jagiellonian University in Kraków)

Room: Lecture hall of Institute of Mathematics An introductory lecture to the sphaleron in the Electroweak model

The SMEFT oscillon

• Andrzej Wereszczyński (Jagiellonian University)

Room: Lecture hall of Institute of Mathematics

Background Adapted Collective Coordinate Models for Kink Dynamics

• Jacek Gatlik (AGH University in Krakow)

Room: Lecture hall of Institute of Mathematics Collective coordinate models reduce field dynamics to a few variables, but their accuracy depends strongly on the ansatz. I will discuss a sequence of examples in which the kink profile is adapted to the local geometry or to spatially and temporally varying coefficients. Starting with radial $\phi^4$ kinks in a Schwarzschild-like geometry, I will show how a metric dependent rescaling combined with a dynamical width gives an accurate reduced description beyond the weak gravity regime. I will then consider sine-Gordon kinks on periodic and non-autonomous backgrounds, where the local background enters directly into a two-coordinate ansatz for the kink position and width. The resulting models reproduce long and nontrivial field trajectories and can also be used to analyse parametrically driven instabilities. Finally, I will discuss the extension to a driven damped $\phi^4$ model and compare width based and internal mode based reductions. These examples show that the structure built into the ansatz, especially the local scale imposed by the background, is often as important as the choice of collective coordinates themselves.

On mechanical properties and stability of isospinning CP^2 solitons

• Sergei Antsipovich (Belarusian State University)

Room: Lecture hall of Institute of Mathematics Isorotating solitons in (2+1)-dimensional CP^2 nonlinear sigma model with a stabilizing potential term were studied. Families of U(1)×U(1) symmetric solutions with topological degrees equal or larger than 1 are found, which have two angular frequencies and are labeled by two (one topological and the other nontopological) winding numbers k1 ≥ k2. The distributions of the corresponding shear forces and pressure were evaluated, along with the stability criteria for these solutions.

A Resonance System between Long and Short Waves

• Kouichi Toda (Toyama Pref. Univ.)

Room: Lecture hall of Institute of Mathematics We study a resonant system that describes the interaction between long and short waves. The system is related to a Sasa–Satsuma-type equation and is obtained by a dimensional reduction of a higher-dimensional model; we also show how it arises within a weakly nonlinear description of wave propagation. Our main focus is on the soliton solutions and their characteristic behavior. Besides ordinary travelling-wave profiles, we find solutions whose envelopes oscillate as they propagate. We further examine the two-soliton interaction and the change in the internal states of the solitons after collision. These results illustrate the rich nonlinear dynamics generated by long and short waves resonance.

Nonlinear sigma models on Kahler C-space and their solitons

• Masato Arai (Yamagata University)

Room: Lecture hall of Institute of Mathematics We construct gauged linear sigma models whose strong gauge coupling limit yields nonlinear sigma models on Kahler C-space. We derive vortex solutions and their moduli space in the gauged linear sigma models.

Topology-Spectral Flow Correspondence for Different Fermion-Soliton Couplings

• Shintaro Yamamoto (Tokyo University of Science)

Room: Lecture hall of Institute of Mathematics Topologically nontrivial solitons often exhibit characteristic fermionic spectra when coupled to Dirac fermions. In many fermion–soliton systems, spectral flow reflects the underlying topology of the soliton. However, it remains unclear which fermion–soliton couplings support this correspondence. In this talk, we approach this problem by analytically investigating several representative fermion–soliton coupling schemes. Our results provide a first step toward a systematic understanding of the role of fermion–soliton couplings.

Quench Dynamics of the axisymmetric Q-balls

• Rin Minekawa (Tokyo University of Science)

Room: Lecture hall of Institute of Mathematics Q-balls are non-topological solitons that are supposed to have emerged in the early era of our universe via the Affleck-Dine mechanism. During the long cosmological evolution, at some period the vacuum drastically may change, like those in the phase transitions. For such environmental shifts on Q-balls, we introduce the concept of "quench" dynamics, which is governed by the change of the scalar potential of the model. More precisely, the quench is achieved by rapidly changing the parameters of the potential. In Q-ball's initial profile as the data of a particular pre-quench potential, we then evolve the system for t≥0 under a different post-quench potential. In this presentation, we will discuss how this sudden change in the potential dramatically affects the stability and dynamical evolution of Q-balls.

Chiral Lump Lattice

• Minoru Eto (Yamagata University)

Room: Lecture hall of Institute of Mathematics TBA

Analysis of self-gravitating fermion systems with NJL-type dynamical mass generation

• Daiki Niiyama (Tokyo University of Science)

Room: Lecture hall of Institute of Mathematics A fermionic many-body system with a current mass can be localized within a finite spatial region solely by gravity [1]. Previous studies have investigated systems incorporating electromagnetic fields [2] and their extensions to multiple-shell configurations [3]. In this work, we formulate an Einstein–Dirac–Maxwell system incorporating a Nambu–Jona-Lasinio (NJL)-type four-fermion interaction. We discuss mass generation through spontaneous chiral symmetry breaking in curved spacetime, and report numerical results on the spatial structure and physical properties of self-gravitating many-fermion systems with dynamically generated mass. [1]F. Finster, J. Smoller, S.T. Yau, Particle-like solutions of the Einstein–Dirac equations. Phys. Rev. D 59, 104020 (1999) [2]F. Finster, J. Smoller, S.T. Yau, Particle-like solutions of the Einstein–Dirac–Maxwell equations. Phys. Lett. A 259, 431–436 (1999) [3]S. Iwasawa, N. Sawado, Multishell Dirac fermions in the Einstein-Dirac system. Phys. Rev. D 112, 064046 (2025)

Decay of Metastable Domain Walls under Thermal Fluctuations

• Davide Chiego (Max Planck Institute for Physics)

Room: Lecture hall of Institute of Mathematics n some theories, defects are metastable and can decay via the nucleation of defects of lower dimensionality through quantum or thermal fluctuations. While at low temperatures the decay is dominated through quantum tunnelling, at higher temperatures thermal decay dominates. Using numerical methods, we simulate defects in a thermal bath at various temperatures and study their thermal decay. In particular, my talk will focus on a 2+1-dimensional model that supports metastable domain walls and vortices connected by these walls. The decay occurs through the nucleation of vortex - anti-vortex pairs along the wall. From a large number of samples, the decay rate is found to be compatible with that expected for a process described by a sphaleron configuration. Studying this model serves as a first step towards understanding how thermal decay impacts the stability of defects in relevant 3+1-dimensional scenarios, such as domain walls bounded by strings in axion models and magnetic monopoles confined by cosmic strings in GUTs. Given the relevance of topological defects in the early Universe, understanding the thermal breaking of such configurations provides important insights into their evolution.