A New Method for Deriving Soliton Design Criteria

A new method for deriving extreme soliton current criteria for offshore engineering applications is described. The primary data source was site specific measurement close to the continental shelf break where metocean criteria were required. A dedicated oceanographic mooring was designed to quantify solitons, with rapidly sampled measurement of seawater temperature and velocities through the vertical. As described in two previous OMAE papers, quantification of soliton velocity profiles was achieved via temperature measurement and theory, with measured velocities playing a secondary role in critical validation. The previous methodology was extended in the present study, with separate contributions quantified from variations in soliton amplitude and water column density structure. The nonlinear Fourier techniques first described in OMAE 2017 were again used to reduce uncertainty in estimates of extreme soliton amplitude. In a new development, the long-term distribution of the density structure contribution was quantified using a calibrated hindcast of seawater temperature. Extreme conditions were defined at the boundary of a MITgcm model domain. This sophisticated model was then used to estimate extreme soliton velocities, through the water column and a few metres above the seabed, at a wide range of shallower target locations.

Самоиндуцированная прозрачность в монослое черного фосфора

A theory of the optical soliton of self-induced transparency (SIT) in a black phosphorus monolayer (phosphorene) has been developed. Explicit analytical expressions describing the surface soliton in phosphorene and other anisotropic two-dimensional materials are obtained. It is shown that the anisotropic phosphorene conductivity leads to exponential damping of the amplitude of the soliton of the surface wave, which strongly depends on the direction of pulse propagation. The maximum damping of the SIT soliton amplitude takes place in the “armchair” direction of phosphorene.

Soliton interactions of a (2+1)-dimensional nonlinear Schrödinger equation in a nonlinear photonic quasicrystal or Kerr medium

Under investigation are the soliton interactions for a (2[Formula: see text]+[Formula: see text]1)-dimensional nonlinear Schrödinger equation, which can describe the dynamics of a nonlinear photonic quasi-crystal or vortex Airy beam in a Kerr medium. With the symbolic computation and Hirota method, analytic bright N-soliton and dark two-soliton solutions are derived. Graphic description of the soliton properties and interactions in a nonlinear photonic quasicrystal or Kerr medium is done. Through the analysis on bright and dark one solitons, effects of the optical wavenumber/linear opposite wavenumber and nonlinear coefficient on the soliton amplitude and width are studied: when the absolute value of the optical wavenumber or linear opposite wavenumber increases, bright soliton amplitude and dark soliton width become smaller; nonlinear coefficient has the same influence on the bright soliton as that of the optical wavenumber or linear opposite wavenumber, but does not affect the dark soliton amplitude or width. Overtaking/periodic interactions between the bright two solitons and overtaking interactions between the dark two solitons are illustrated. Overtaking interactions show that the bright soliton with a larger amplitude moves faster and overtakes the smaller, while the dark soliton with a smaller amplitude moves faster and overtakes the larger. When the absolute value of the optical wavenumber or linear opposite wavenumber increases, the periodic-interaction period becomes longer. All the above interactions are elastic. Through the interactions, soliton amplitudes and shapes keep invariant except for some phase shifts.

Solitons for a forced generalized variable-coefficient Korteweg–de Vries equation for the atmospheric blocking phenomenon

Investigation is given to a forced generalized variable-coefficient Korteweg–de Vries equation for the atmospheric blocking phenomenon. Applying the double-logarithmic and rational transformations, respectively, under certain variable-coefficient constraints, we get two different types of bilinear forms: (a) Based on the first type, the bilinear Bäcklund transformation (BT) is derived, the [Formula: see text]-soliton solutions in the Wronskian form are constructed, and the [Formula: see text]- and [Formula: see text]-soliton solutions are proved to satisfy the bilinear BT; (b) Based on the second type, via the Hirota method, the one- and two-soliton solutions are obtained. Those two types of solutions are different. Graphic analysis on the two types shows that the soliton velocity depends on [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text], the soliton amplitude is merely related to [Formula: see text], and the background depends on [Formula: see text] and [Formula: see text], where [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] are the dissipative, dispersive, nonuniform and line-damping coefficients, respectively, and [Formula: see text] is the external-force term. We present some types of interactions between the two solitons, including the head-on and overtaking interactions, interactions between the velocity- and amplitude-unvarying two solitons, between the velocity-varying while amplitude-unvarying two solitons and between the velocity- and amplitude-varying two solitons, as well as the interactions occurring on the constant and varying backgrounds.

Obliquely propagating electron acoustic solitons in magnetized plasmas with nonextensive electrons

The problem of small amplitude electron-acoustic solitary waves (EASWs) is discussed using the reductive perturbation theory in magnetized plasmas consisting of cold electrons, hot electrons obeying nonextensive distribution and stationary ions. The presented investigation shows that the presence of nonextensive distributed hot electrons (due to the effects of long-range interactions) causes a reduction in the soliton amplitude while its width increases. The effects of the population ratio of hot to cold electrons and also the effects of the presence of magnetic field in this situation are also discussed.

SOLITON STEERING IN A RAMP WAVEGUIDE WITH NONLOCAL NONLINEARITY

We present an analytical and numerical investigation of a spatial soliton propagating in a waveguide with ramp linear refractive index profile (ramp waveguide) and nonlocal nonlinearity. It is shown analytically by equivalent particle approach and numerically by implicit Crank-Nicolson scheme that in a ramp waveguide with local nonlinearity, the soliton experiences negative acceleration along the waveguide where its refractive index decreases linearly. On the other hand, if the soliton propagates in a uniform medium with nonlocal nonlinear response then it will experience a self-bending in the positive direction where the bending level depends on the soliton amplitude as well as on the strength of nonlocality. By combining these two effects, rich dynamics of soliton can be achieved. In this case, the soliton may oscillate inside the waveguide, move to the left or to the right part of the waveguide or even be trapped. Such soliton steering can be controlled by the soliton amplitude or by its initial position.