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General equations describing shear displacements in incompressible hyperelastic materials, holding for an arbitrary form of strain energy density function, are presented and applied to the description of nonlinear Love-type waves…
In this work, we show that collisions of one type of nonlinear wave can lead to generation of a different kind of nonlinear wave. Specifically, we demonstrate the formation of topological solitons (or transition waves) via collisions of…
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…
The linear and nonlinear surface waves propagating along the interface separating isotropic conventional and uniaxially anisotropic left-handed materials is investigated. The conditions of the existence of surface TM-modes is determined. It…
The nonlinear dispersive wave equation inside the cylindrical elastic rod is derived by applying the Navier-Bernoulli hypothesis and Love's relation in \cite{5}. The elastic rod is assumed to be composed of the Murnaghan's materials such as…
A theory of an optical vector pulsing soliton of self-induced transparency in an ensemble of semiconductor quantum dots is investigated. It is shown that a distribution of the excitonic ground-state transition dipole moments of the quantum…
The excitation of soliton states in optical layers exhibiting Kerr nonlinearities is theoretically investigated. The optical transmission coefficient is obtained as a function of the nonlinearity power of an incident monochromatic…
A theory of self-induced transparency of surface TM-mode propagating along a interface separating conventional and left-handed metamaterials is developed. A transition layer sandwiched between connected media is described using a model of a…
We develop the analytical method of field momenta for analyzing the dynamics of optical vector solitons in photorefractive nonlinear media. First, we derive the effective evolution equations for the parameters of multi-component solitons…
The results of recent experiments [1] on observing soliton lattices and their dislocations in vertical cylindrical channels filled with immiscible fluids with strongly different viscosities and but slightly different densities are…
We study trapping and propagation of a matter-wave soliton through the interface between uniform medium and a nonlinear optical lattice (NOL). Different regimes for transmission of a broad and a narrow soliton are investigated. Reflections…
A theory of optical nonresonance vector pulsing solitons in a Kerr media is considered. By using the perturbative reduction method the wave equation is transformed to the coupled nonlinear Schrodinger equations. The profile of the optical…
Fundamental solitons pinned to the interface between three semi-infinite one-dimensional nonlinear dynamical chains, coupled at a single site, are investigated. The light propagation in the respective system with the self-attractive on-site…
We investigate light beam propagation along the interface between linear and nonlinear media with parity-time PT symmetry, and derive an equation governing the beam propagation. A novel class of two-dimensional PT surface solitons are found…
In the context of the finite elasticity theory, we consider a model for compressible solids called 'compressible neo-Hookean material'. We show how finite-amplitude inhomogeneous plane wave solutions and finite-amplitude unattenuated…
We address the properties of two-dimensional surface solitons supported by the interface of a waveguide array whose nonlinearity is periodically modulated. When the nonlinearity strength reaches its minima at the points where the linear…
We report experimental results and study theoretically soliton formation and propagation in an airfilled acoustic waveguide side loaded with Helmholtz resonators. Our theoretical approach relies on a transmission-line description of this…
We study the propagation of quasi-discrete microwave solitons in a nonlinear left-handed coplanar waveguide coupled with split ring resonators. By considering the relevant transmission line analogue, we derive a nonlinear lattice model…
A study of the coupling between lattice ion vibrations and electron waves in a piezoelectric semiconductor quantum plasma is presented. The nonlinearities have been analyzed, and solitons have been studied. The theory is built using the…
We discuss the dynamics of interacting dark-bright two-dimensional vector solitons in multicomponent immiscible bulk Bose-Einstein condensates. We describe matter-wave molecules without a scalar counterpart that can be seen as bound states…