Pattern Formation and Solitons
In the scalar nonlinear Schrodinger equation, an Akhmediev breather (AB) is dominated by a frequency that lies inside the modulation instability gain band. This exactly correspondence between instability and breathers is challenged in…
We consider quasi-one-dimensional (Q1D) continuous waves (CWs) in the two-dimensional (2D) optical system with the cubic-quintic nonlinearity and a Q1D potential trough. In the case of a smooth trough profile, we confirm the known…
Frequency combs, evenly spaced spectral lines locked to one fundamental frequency, are well known in optics and have also been found in phononic, magnonic, ferroelectric, and cosmological systems, but have not yet been studied in…
We investigate a (2+1)-dimensional nonlinear spin system containing an effective spin-current transport term. Based on its integrable structure, exact magnetic lump solutions are constructed on a rotating spin background, including both…
Phononic frequency combs offer a rich platform for nonlinear sensing, yet how their observable properties respond to changes in physical parameters remains poorly understood. Using a reduced two-mode autoparametric resonance model, we…
Width-balance conditions at a junction are often associated with reflectionless transmission, or transparency, in some one-dimensional wave models on networks. We show that, on cyclic networks, this identification is incomplete: local…
We investigate the interaction of small-amplitude waves called phonons, with an initially static kink in an exceptional discretization of the $\phi^4$ model that is free of the Peierls-Nabarro potential. Phonons are generated by a localized…
Dissipative solitons constitute a robust class of self-localized nonlinear states sustained by the dynamic balance between nonlinearity and gain-loss, possessing an intrinsic stability that stems from their fundamental attractor nature.…
We investigate the Thouless pumping dynamics of nonlinear gap solitons and attempt to realize topological Chern number switching by modulating nonlinear parameters and varying the ramping rate of the relative phase between periodic…
We formulate a general system of kinetic equations for a non-stationary two-dimensional gas of elastically interacting line solitons and apply it to the description of a soliton gas governed by the Kadomtsev-Petviashvili II (KPII) equation.…
In the present work we analyze traveling and dispersive shock waves of a two-dimensional Fermi-Pasta-Ulam-Tsingou lattice. In the first part of the paper, using variational techniques we prove the existence of both periodic and solitary…
In a recent work we studied the first nonlinear stage of modulation instability (NLSMI) of x-periodic anomalous (rogue, freak, extreme) waves (AWs) of physically relevant multidimensional (generalizations of the focusing) nonlinear…
We investigate the dynamical mechanisms underlying the contrasting nonlinear Floquet spectral evolutions observed in viscous and nonlinear mean-flow damped higher-order nonlinear Schr"odinger systems. Motivated by the persistent organized…
Three-wave interactions (or resonant triads) are the lowest-order nonlinear interaction in pattern formation and arise between waves with different orientations when the sum of two wavevectors equals a third one. When a pattern has only one…
We investigate the emergence of chaotic dynamics in collective-coordinate reductions of a driven and spatially modulated $\phi^4$ field describing the motion of topological kinks. Focusing on finite-dimensional effective models, we consider…
We study of the formation of pattern-forming fronts in the presence of a rigidly-propagating parameter ramp which is slowly-varying in space. In the context of the prototypical supercritical complex Ginzburg-Landau equation, we show that…
We explore pattern formation in an active fluid system involving two chemical species that regulate active stress: a fast-diffusing species ($A$) and a slow-diffusing species ($I$). The growth of species $A$ is modelled using a nonlinear…
Non-Hermitian lattices with non-reciprocal couplings under open boundary conditions are known to possess linear modes exponentially localized on one edge of the chain. This phenomenon, dubbed non-Hermitian skin effect, induces all input…
In the present work, we revisit the Adlam-Allen (AA) model in order to investigate its numerically observed rarefaction and dispersive shock waves that arise in numerical simulations of the Riemann problem associated with the model. On the…
Extending a recent effective theory formulation for the dynamics of kinks in the sine-Gordon model [1], we propose an analogous effective description of $\phi^4$ kinks. Three different reduced models based on the kink position, width and…