Pattern Formation and Solitons
In this paper, we report on the generation and propagation of traveling pulses in a homogeneous network of diffusively coupled, excitable, slow-fast dynamical neurons. The spatially extended system is modelled using the nearest neighbor…
Real world systems comprised of coupled oscillators have the ability to exhibit spontaneous synchronization and other complex behaviors. The interplay between the underlying network topology and the emergent dynamics remains a rich area of…
Compressed cylindrical shells are common in our daily life, such as the diamond shape in rolled-up sleeves, crumpled aluminum cans, and retreated package of now defunct drinking straws. The kind of deformation is formally called the…
Synchronization of mobile oscillators occurs in numerous contexts, including physical, chemical, biological and engineered systems. In vertebrate embryonic development, a segmental body structure is generated by a population of mobile…
In this paper, we employ a combination of analytical and numerical techniques to investigate the dynamics of lattice envelope vector soliton solutions propagating within a one-dimensional chain of flexible mechanical metamaterial. To model…
In engineering crystal plasticity inelastic mechanisms correspond to tensorial zero-energy valleys in the space of macroscopic strains. The flat nature of such valleys is in contradiction with the fact that plastic slips, mimicking…
In honor of the great Russian mathematician A. N. Kolmogorov, we would like to draw attention in the present paper to a curious mathematical observation concerning fractional differential equations describing physical systems, whose time…
We present the adiabatic theory of dissipative solitons (DS) of complex cubic-quintic nonlinear Ginzburg-Landau equation (CQGLE). Solutions in the closed analytical form in the spectral domain have the shape of Rayleigh-Jeans distribution…
We consider a version of the classical Hamiltonian Fermi-Pasta-Ulam (FPU) problem with a trilinear force-strain relation of soft-hard-soft type that is in general non-symmetric. In addition to the classical spatially localized solitary…
We study the time-fractional Ivancevic option pricing model and the coupled nonlinear volatility and option price model via both modulational instability (MI) analysis and direct simulations. For the coupled volatility and option pricing…
The skin of a cephalopod forms a dazzling array of patterns made by chromatophores, elastic sacs of pigment that can be expanded by muscles to reveal their color. Tens of thousands of these chromatophores can work together to generate a…
The moment quantities associated with the nonlinear Schrodinger equation offer important insights towards the evolution dynamics of such dispersive wave partial differential equation (PDE) models. The effective dynamics of the moment…
We investigate propagation of J soliton sequences in a nonlinear optical waveguide array with generic weak Ginzburg-Landau (GL) gain-loss and nearest-neighbor (NN) interaction. The propagation is described by a system of J perturbed coupled…
We introduce a system of propagation equations for the fundamental-frequency (FF) and second-harmonic (SH) waves in the bulk waveguide with the effective fractional diffraction and quadratic (chi ^(2)) nonlinearity. The numerical solution…
The modulation instability (MI) is responsible for the disintegration of a regular nonlinear wave train and can lead to strong localizations in a from of rogue waves. This mechanism has been studied in a variety of nonlinear dispersive…
The propagation of water waves of finite depth and flat bottom is studied in the case when the depth is not small in comparison to the wavelength. This propagation regime is complementary to the long-wave regime described by the famous KdV…
Our analysis suggests strongly that stationary pulses exist in nonlinear media with second-, third-, and fourth-order dispersion. A theory, based on the variational approach, is developed for finding approximate parameters of such solitons.…
An autoresonant approach for exciting space-time quasicrystals in Bose-Einstein condensates is proposed by employing two-component chirped frequency parametric driving or modulation of the interaction strength within Gross-Pitaevskii…
Nonlinear Schr\"{o}dinger equation was originally derived in nonlinear optics as a model for beam propagation, which naturally requires its application in cylindrical coordinates. However, the derivation was done in the Cartesian…
We prove the existence of a class of time-localized and space-periodic breathers (called q-gap breathers) in nonlinear lattices with time-periodic coefficients. These q-gap breathers are the counterparts to the classical space-localized and…