Pattern Formation and Solitons
Surface stiffnesses engender steady patterns of Faraday waves (FWs), so called hydrodynamic crystals as correspond to ordered wave lattices made of discrete subharmonics under monochromatic driving. Mastering rules are both inertia-imposed…
We consider a version of the classical Hamiltonian FPU (Fermi-Pasta-Ulam) problem with nonlinear force-strain relation in which a hardening response is taken over by a softening regime above a critical strain value. We show that in addition…
Neural Cellular Automata (NCA) are a powerful combination of machine learning and mechanistic modelling. We train NCA to learn complex dynamics from time series of images and PDE trajectories. Our method is designed to identify underlying…
In recent years, nonreciprocally coupled systems have received growing attention. Previous work has shown that the interplay of nonreciprocal coupling and Goldstone modes can drive the emergence of temporal order such as traveling waves. We…
We study solitary wave solutions for the nonlinear Schr\"odinger equation perturbed by the effects of third-, and fourth-order dispersion, maintaining a wavenumber gap between the solitary waves and the propagation constant. We numerically…
This work analyzes bifurcation delay and front propagation in the one-dimensional real Ginzburg-Landau equation (RGLE) with periodic boundary conditions on monotonically growing or shrinking domains. First, we obtain closed-form expressions…
Within the framework of numerical simulations, we study the gyrotron dynamics under conditions of a significant excess of the operating current over the starting value, when the generation of electromagnetic pulses with anomalously large…
Spatially extended versions of the cyclic-dominance Rock-Paper-Scissors model have traveling wave (in one dimension) and spiral (in two dimensions) behavior. The far field of the spirals behave like traveling waves, which themselves have…
We study the dynamics of two-dimensional nonlinear ion-ion hybrid waves propagating perpendicular to an external magnetic field in plasmas with two ion species. We derive nonlinear equations for the envelope of electrostatic potential at…
In the recent work "Non-reciprocal topological solitons in active metamaterials" (see arXiv:2312.03544v1), for an analytical understanding of the system under consideration, the authors derive an ordinary differential equation for the…
We consider motion of a "magnetic'' soliton in two-component condensates along a non-uniform and time-dependent backgrounds in framework of the Hamiltonian mechanics. Our approach is based on generalization of Stokes' remark that soliton's…
Pattern dynamics on curved surfaces are ubiquitous. Although the effect of surface topography on pattern dynamics has gained much interest, there is a limited understanding of the roles of surface geometry and topology in pattern dynamics.…
The existence and properties of envelope solitary waves on a periodic, traveling wave background, called traveling breathers, are investigated numerically in representative nonlocal dispersive media. Using a fixed point computational…
Long range interactions between dark vectorial temporal cavity solitons are induced though the spontaneous symmetry breaking of orthogonally polarized fields in ring resonators. Turing patterns of alternating polarizations form between…
Motivated by the work of J.K.~Jang et al., Nat.~Commun.~{\bf 6}, 7370 (2015), where the authors experimentally tweeze cavity solitons in a passive loop of optical fiber, we study the amenability to tweezing of cavity solitons as the…
Most of previously reported dark-bright solitons admit identical width for the two components in both theoretical and experimental studies. We report dark-bright solitons can admit strikingly different widths, and derive a family of…
This study investigates transient wave dynamics in Turing pattern formation, focusing on waves emerging from localised disturbances. While the traditional focus of diffusion-driven instability has primarily centred on stationary solutions,…
This paper explores the analytical approach for obtaining the multiple solutions of three-wave interacting system in (1+1) dimensions. We present a novel approach by expressing the wave solutions in terms of Jacobi elliptic functions and…
We analyze the implication of tristability on localization phenomena in one-dimensional extended dissipative systems. In this context, localized states appear due to the interaction and locking of front waves connecting different extended…
In this paper, the vibration energy localization in coupled nonlinear oscillators is investigated, based on the creation of standing solitons. The main objective is to establish a design methodology for mechanical lattices using the…