Pattern Formation and Solitons Papers of the Week

Here, we reveal a class of stable dissipative solitons enabled by the pure-high-even-order dispersion (PHEOD), with dispersion orders m=4, 6, 8, and 10.

We study rogue wave formation in the dam-break problem for the Kundu--Eckhaus equation with deterministic and randomly perturbed box initial data.

To this end, this article investigates a Vicsek-Kuramoto model with distance-dependent higher-order interactions and obtains analytical results, albeit under certain assumptions, that characterize its collective dynamics.

We show that nonlinear interactions enable all-optical control over edge-state dissipation in a laser-written Floquet topological insulator periodically coupled to a photonic bath.

A binary Bose--Einstein condensate in an elongated trap supports unpolarized excited states, in which both components share the same spatial profile. Within mean-field theory we show that the interspecies repulsion at which these states demix rises with the excitation level.

Rational solutions of partial differential equations (PDEs) are notoriously difficult to approximate via spectral Fourier methods due to their algebraically slow decay rate. In this work we discuss approximating rational PDE solutions in a basis of orthogonal functions known as the Christov functions, allowing for the computation of its spectrum via the fast Fourier transform.

In this work, a simple analytical model for a new type of magnetic hopfions --- ``concentric'' ones --- is constructed and solved.

In this paper we investigate the links between undulation amplitude and pattern dynamics, with the goal of understanding how the terrain impacts the resilience of the vegetation.

We study a single-species vegetation model in which a strong Allee effect acts locally and competition acts through a nonlocal kernel, and we describe the kernel with the one-parameter family of q-Gaussians, which goes from compact support to power-law tails.

We investigate the interaction of dissipative Kerr solitons in two nearly identical coherently driven, coupled microresonators in the presence of third-order dispersion (TOD).

We develop a Fourier-based framework that relates waveform symmetry, regularity, and modulation to the structure of overtone- and sideband frequency combs.

We develop the first analytical framework for synchronization in non-fast-switching networks of saddle-focus continuous-time oscillators.

We obtain exact solutions of the nonlinear Dirac (NLD) equation in $1+1$ dimensions of the form $\psi(x,t) = e^{-i\omega t} \psi(x)$ for all possible combinations of scalar-scalar (SS), vector-vector (VV) and pseudoscalar-pseudoscalar (PP) interactions at nonlinearity parameter $\kappa = 1$, which corresponds to the most general 4-Fermion interactions.

We investigate three-dimensional light bullets (LBs) in an optically injected, vertically emitting Kerr-Gires-Tournois interferometer operating in the normal dispersion regime.

However, a rigorous analytical understanding of the underlying instability mechanisms in the subcritical regime has remained open. In this work, we provide a theoretical answer to these numerical findings by establishing the spectral instability of the fundamental soliton solution.

We investigate effects of longitudinally varying nonlinearity on periodically distributed amplification systems in optical fibres.

We investigate two-dimensional Couette flow between parallel plates as a model of protoplasmic streaming in plant cells using a combined Langevin and Navier?Stokes simulation.

We identify two families of stationary solutions, $\Psi_\pm$, whose existence is determined by two conditions: one involving the nonlinearity exponent~$\kappa$ and the spatial dimension~$N$, and another involving the forcing amplitude~$r$ and the damping coefficient~$\rho$. By linearising around these solutions and introducing a convenient parametrisation through~$\varepsilon$, we reduce the stability problem to a dissipationless eigenvalue problem for two Schrödinger-type operators, $L_0$ and $L_1$.