Pattern Formation and Solitons
We present exact N-soliton optical pulses riding on a continuous-wave (c.w.) beam that propagate through and interact with a two-level active optical medium. Their representation is derived via an appropriate generalization of the inverse…
Rogue waves on the periodic background are considered for the nonlinear Schrodinger (NLS) equation in the focusing case. The two periodic wave solutions are expressed by the Jacobian elliptic functions dn and cn. Both periodic waves are…
A conceptually new notion of hydrodynamic optical soliton tunneling is introduced in which a dark soliton is incident upon an evolving, broad potential barrier that arises from an appropriate variation of the input signal. The barriers…
We study the effect of domain growth on the orientation of striped phases in a Swift-Hohenberg equation. Domain growth is encoded in a step-like parameter dependence that allows stripe formation in a half plane, and suppresses patterns in…
In traffic systems, cooperative driving has attracted the researchers attentions. A lot of works attempt to understand the effects of cooperative driving behavior and/or time delays on traffic flow dynamics for specific traffic flow model.…
We demonstrate the occurrence of anomalous diffusion of dissipative solitons in a `simple' and deterministic prototype model: the cubic-quintic complex Ginzburg-Landau equation in two spatial dimensions. The main features of their dynamics,…
We demonstrate that the amplitudes of optical solitons in nonlinear multisequence optical waveguide coupler systems with weak linear and cubic gain-loss exhibit large stable oscillations along ultra-long distances. The large stable…
We study the (1+1)-dimensional quasiperiodic multicolor solitons due to cascading quadratic nonlinear response in generalized one-dimensional quasiperiodic optical superlattice waveguides and show that the dynamic equations describing the…
We study pattern formation in a 2-D reaction-diffusion (RD) sub-cellular model characterizing the effect of a spatial gradient of a plant hormone distribution on a family of G-proteins associated with root-hair (RH) initiation in the plant…
A subcritical pattern-forming system with nonlinear advection in a bounded domain is recast as a slow-fast system in space and studied using a combination of geometric singular perturbation theory and numerical continuation. Two types of…
In the present work we consider a model that has been proposed at the continuum level for self-defocusing nonlinearities in atomic BECs in order to capture phenomenologically the loss of condensate atoms to thermal ones. We explore the…
We demonstrate a possibility to make rogue waves (RWs) in the form of the Peregrine soliton (PS) and Kuznetsov-Ma breathers (KMBs) effectively stable objects, with the help of properly defined dispersion or nonlinearity management applied…
Fronts propagating in two-dimensional advection-reaction-diffusion (ARD) systems exhibit rich topological structure. When the underlying fluid flow is periodic in space and time, the reaction front can lock to the driving frequency. We…
We address the problem of a front propagation in chains with a bi-stable nondegenerate on-site potential and a nonlinear gradient coupling. For a generic nonlinear coupling, one encounters a special regime of transitions, characterized by…
In the aerospace industry the trend for light-weight structures and the resulting complex dynamic behaviours currently challenge vibration engineers. In many cases, these light-weight structures deviate from linear behaviour, and complex…
This work studies the acoustic band structure of tensegrity metamaterials, and the possibility to tune the dispersion relation of such systems by playing with local and global prestress variables. Building on established results of the…
In this work, we study the existence of low amplitude four-site phase-shift multibreathers for small values of the coupling $\epsilon$ in Klein-Gordon (KG) chains with interactions longer than the classical nearest-neighbour ones. In the…
We consider a one-dimensional discrete nonlinear Schr{\"o}dinger (dNLS) model featuring interactions beyond nearest neighbors. We are interested in the existence (or nonexistence) of phase-shift discrete solitons, which correspond to…
We develop a general approach to the description of dispersive shock waves (DSWs) for a class of nonlinear wave equations with a nonlocal Benjamin-Ono type dispersion term involving the Hilbert transform. Integrability of the governing…
We propose a novel, analytically tractable, scenario of the rogue wave formation in the framework of the small-dispersion focusing nonlinear Schr\"odinger (NLS) equation with the initial condition in the form of a rectangular barrier (a…