Nonlinear surface waves propagating along composite waveguide consisting of nonlinear defocusing media separated by interfaces with nonlinear response

The nonlinear surface waves propagating along the ultra-thin-film layers with nonlinear properties separating three nonlinear media layers are considered. The model based on a stationary nonlinear Schrödinger equation with a nonlinear potential modeling the interaction of a wave with the interface in a short-range approximation is proposed. We concentrated on effects induced by the difference of characteristics of the layers and their two interfaces. The surface waves of three types exist in the system considered. The dispersion relations determining the dependence of surface waves energy on interface intensities and medium layer characteristics are obtained and analyzed. The localization energy is calculated in explicit form for many difference cases. The conditions of the wave localization on dependence of the layer and interface characteristics are derived. The surface waves with definite energies in specific cases existing only in the presence of the interface nonlinear response are found. All results are obtained in an explicit analytical form.

Water wave resonance in a circular oscillating channel

<p>Nonlinear surface waves in the form of tidal bores can have a profound impact on the flow in rivers and estauries. The waves can also be studied experimentally in a specially designed periodic channel at BTU Cottbus-Senftenberg [1],[2]. We hence analyze these surface waves in this narrow circular channel partially filled with water and compare the data with numerical simulations. The flow in the channel is blocked by a barrier and the channel oscillates in azimuthal direction with variable frequency,  maintaining the same maximum velocity. The response in terms of wave shape, maximum amplitude and root mean square of the surface deviations are numerically investigated and compared with experiments. Note that for the experimental setup a number of maximum eight ultrasound sensors can provide the local height evolution. Due to the oscillations, the barrier produces wave trains or hydraulic jumps which then propagate inside the channel. Reflections, damping and collisions take place. Some frequencies are  favourised and in the first approximation can also be calculated using a shallow water model. How will be seen, only the odd multiples of the basic frequency produce high answers (resonances).<br><br>[1] I.D. Borcia, R. Borcia, Wenchao Xu, M. Bestehorn, S. Richter, and U. Harlander. Undular bores in a large circular channel. European Journal of Mechanics - B/Fluids, 79, 67-73, 2020.<br><br>[2] I.D. Borcia, R. Borcia, S. Richter, Wenchao Xu, M. Bestehorn, and U. Harlander. Horizontal Faraday instability in a circular channel. Proceedings in Applied Mathematics and Mechanics (PAMM), 19, , 2019.</p>

Нелинейные поверхностные волны в симметричной трехслойной структуре из оптических сред с различными механизмами формирования нелинейного отклика

The propagation of surface TM waves in a three-layer structure, which is a crystal thickness plate with a focusing nonlinearity of a Kerr type, sandwiched between uniaxial photorefractive crystals with a diffusion mechanism for the formation of nonlinearity is considered. Nonlinear surface waves with different attenuation patterns can propagate along the interfaces between the layers. Waves of one type attenuate with distance from the interfaces without oscillations into the depth of the outer layers of photorefractive crystals, and the waves of other type attenuate with oscillations. Wave profiles can have two forms of symmetry about the center of a three-layer structure: symmetric and antisymmetric. The two waves with a symmetric distribution exist with nonperiodic damping and the damping without oscillations. The waves only with antisymmetric distribution exist with nonperiodic damping and the damping without oscillations. The dependences of the propagation constant on the characteristics of the layered structure for the long-wave mode of surface wave propagation are found in an explicit analytical form. The conditions for their existence are indicated.

Поверхностные волны на границе фоторефрактивного кристалла и среды с положительной керровской нелинейностью

The types of nonlinear surface waves of extraordinary polarization that occur at the interface between a photorefractive crystal and a medium with positive Kerr nonlinearity are described. It is shown that nonlinear surface waves of an asymmetric profile of two types can exist in such a system. The waves of the first type decay when moving away from the interface without oscillations both in the depth of the photorefractive crystal and in the Kerr crystal, and the waves of the second type decay in the depth of the photorefractive crystal with oscillations. Dispersion relations are obtained, and the conditions for the existence of all the described types of waves are indicated depending on the optical characteristics of the crystals.

Распространение поверхностных волн вдоль границы фоторефрактивного кристалла с нелинейным дефокусирующим покрытием

A composite waveguide structure, which is a crystal with a diffusion mechanism for the formation of a nonlinear photorefractive response, the surface of which is coated with a non-linear Kerr defocusing type, is considered. It is shown that there exist TM polarized nonlinear surface waves of two types, which differ in the range of existence and the profile of field decay. The propagation modes of nonlinear surface waves are determined in which the field intensity can be maximum or minimum near the surface or at the boundary of the coated crystal.

Nonlinear surface waves propagating along the composite waveguide consisting of self-focusing slab between defocusing media separated by interfaces with nonlinear response

The model of the composite symmetric waveguide consisting of self-focusing slab between defocusing nonlinear media separated by interfaces characterized by own nonlinearity response is proposed. Two new types of nonlinear surface waves propagating along it with anti-phase amplitude oscillations at interface planes are found. The frequencies of the nonlinear surface waves existing near the interfaces with the nonlinear response only are calculated analytically. The conditions of the surface wave existence are found. The frequencies and localization distances of the surface waves in dependence on nonlinearity waveguide parameters, slab width and interface characteristics are analyzed.