Related papers: Nonlinear Localized Coherent Spectrum of Beam-Beam…
This paper develops a harmonic-domain framework for systems with variable fundamental frequency. A variable-frequency sliding Fourier decomposition is introduced in the phase domain, together with necessary and sufficient conditions for…
Complex systems are often driven by higher-order interactions among multiple units, naturally represented as hypergraphs. Understanding dependency structures within these hypergraphs is crucial for understanding and predicting the behavior…
In this paper, we suggest a new Heterogeneous Multiscale Method (HMM) for the Helmholtz equation with high contrast. The method is constructed for a setting as in Bouchitt\'e and Felbacq (C.R. Math. Acad. Sci. Paris 339(5):377--382, 2004),…
The (2+1)-dimensional higher-order Broer-Kaup (HBK) system is studied by nonlocal symmetry method and consistent tanh expansion (CTE) method in this paper. Some exact interaction solutions among different nonlinear excitations such as…
It is shown that the mean-field description of a boson-fermion mixture with a dominating fermionic component, loaded in a one-dimensional optical lattice, is reduced to the nonlinear Schr\"{o}dinger equation with a periodic potential and…
We show a procedure for engineering effective interactions between two modes in a bimodal cavity. Our system consists of one or more two-level atoms, excited by a classical field, interacting with both modes. The two effective Hamiltonians…
We consider a two-component linearly-coupled system with the intrinsic cubic nonlinearity and the harmonic-oscillator (HO) confining potential. The system models binary settings in BEC and optics. In the symmetric system, with the HO trap…
Nonlinear contact dynamics are widely regarded as intrinsically nonlinear systems whose behaviour depends strongly on geometry and impact conditions. Here we show that any one-dimensional conservative contact system satisfying monotone…
In the age of information explosion, the conventional optical communication protocols are rapidly reaching the limits of their capacity, as almost all available degrees of freedom (e.g., wavelength, polarization) for division multiplexing…
The observed hemispherical asymmetry in CMB map can be explained by modulation from a long wavelength super horizon mode which non-linearly couples to the CMB modes. We address the criticism in [1] about the role of non-Gaussianities in…
In our earlier work on harmonic generation with complex light [Nature Communications 15, 6878 (2024)], we demonstrated how the harmonic spectrum of a complex laser beam in a nonlinear medium can be obtained through the judicious application…
The aim of this paper is to explore the relationship between invariant cones and nonlinear normal modes in piecewise linear mechanical systems. As a key result, we extend the invariant cone concept, originally established for homogeneous…
After a brief comprehensive review of old and new results on the well known Fermi-Pasta-Ulam (FPU) conservative system of $N$ nonlinearly coupled oscillators, we present a compact linear mode representation of the Hamiltonian of the FPU…
Nonlinear propagation of signals in single-mode fiber is well understood, and is typically observed by measuring the temporal profile or optical spectrum of an emerging signal. In multimode fibers, the nonlinearity has both a spatial and a…
Measuring the mechanical response of liquid interfaces without direct contact remains a major experimental challenge, particularly in liquid-liquid systems where no solid reference exists. Here, we develop a frequency-modulation atomic…
Coherent beam-beam tune shift of unsymmetrical beam-beam interactions was studied experimentally and numerically in HERA where the lepton beam has a very large beam-beam parameter (up to $\xi_y=0.272$). Unlike the symmetrical case of…
Boundary feedback stabilisation of linear port-Hamiltonian systems on an interval is considered. Generation and stability results already known for linear feedback are extended to nonlinear dissipative feedback, both to static feedback…
The effects caused by nonresonant nonlinear interaction between noncollinear self-focusing beams are considered in 2D optical samples using multi-scale analysis. The analytical expression for the beams trajectories shift due to the mutual…
Coherent structures are solutions to reaction-diffusion systems that are time-periodic in an appropriate moving frame and spatially asymptotic at $x=\pm\infty$ to spatially periodic travelling waves. This paper is concerned with sources…
Structured light is routinely used in free space optical communication channels, both classical and quantum, where information is encoded in the spatial structure of the mode for increased bandwidth. Unlike polarisation, the spatial…