A generalized super AKNS hierarchy associated with orthosymplectic Lie superalgebra OSP(2,2) and its super bi-Hamiltonian structures

For the orthosymplectic Lie superalgebra $\text{◂⋅▸}OSP(2,2)$, we choose a set of basis matrices. A linear combination of those basis matrices presents a spatial spectral matrix. The compatible condition of the spatial part and the corresponding temporal parts of the spectral problem leads to a generalized super AKNS (GSAKNS) hierarchy. By making use of the supertrace identity, the obtained GSAKNS hierarchy can be written as the super bi-Hamiltonian structures.     

A supersymmetric Sawada-Kotera equation

A new supersymmetric equation is proposed for the Sawada-Kotera equation. The integrability of this equation is shown by the existence of Lax representation and infinite conserved quantities and a recursion operator.     

Stabilization of spatiotemporal solitons in second-harmonic-generating media

We report the results of a systematic analysis of the existence and stability of spatiotemporal (two-dimensional) solitons (STSs) in the model of a planar waveguide with the intrinsic χ⁽²⁾ nonlinearity. Fundamental obstacles to the creation of STSs under physically realistic conditions are the normal sign of the group-velocity dispersion (GVD) at the second harmonic (SH), and the significant group-velocity mismatch (GVM) between the SH and fundamental-frequency (FF) components. To construct STS solutions in a numerical form, we adjust the iterative method, which was recently used for finding temporal (one-dimensional) χ⁽²⁾ solitons in a similar setting. We identify effective existence borders for the STSs, within which the energy loss to the generation of extended “tails” in the SH component (due to the normal sign of the GVD) is negligible. It is demonstrated that the existence region can be made much broader by means of the GVD-management and GVM-management techniques. We also explore interactions between the STSs, and find robust two-soliton bound states, with a moderate separation in the longitudinal (temporal) direction. Head-on collisions between the STSs are always destructive.     

QED corrections and chemical properties of Eka-Hg

In this paper, we present a family of coupled higher-order nonlinear Schr?dinger equation describing the optical soliton pulse propagating in inhomogeneous optical fiber media. The exact N-soliton solution and its characteristics of stabilities and novel elastic collision properties are studied in detail. As an example, we give the relative numerical evolutions by a soliton control system to discuss the pulses propagation characteristics.     

Investigation of Ti/TiN multilayered films in a reactive mid-frequency dual-magnetron sputtering

Influence of the process parameters like (i) sputtering gas pressure, (ii) target current, (iii) substrate bias voltage and (iv) substrate temperature of a reactive mid-frequency dual-magnetron sputtering on (a) surface defects and (b) mechanical properties of Ti/TiN multilayered films was investigated. The forming mechanisms of the observed droplets and craters were analyzed. Results showed when: (1) pressure of Ar/N₂ gases PAr/N₂ was at 0.31 Pa and substrate temperature was in certain range, the size and the density of the surface defects on the TiN films tended to decrease with increasing the target current and the pulsed bias voltage; (2) the optimal deposition parameters for accomplishing fewer surface defects were used, increasing the thickness of the Ti buffer layer decreased the microhardness in certain level, and the adhesion was firstly increased and then decreased as thickness reaching and/or beyond a critical value. Results also showed that selection of optimized process parameters evidently minimized the surface defects and improved the mechanical properties of the film.     

Exact chirped gray soliton solutions of the nonlinear Schrödinger equation with variable coefficients

In this paper, we consider the nonlinear Schrödinger equation with variable coefficients, and by using direct transformation of variables and functions, the explicit chirped gray one- and two-soliton solutions are presented. Based on the exact solutions, we in detail analyze the propagation characteristics of the chirped gray soliton, including the stability against either the deviation from integrable condition or the initial perturbation, and interaction between the chirped gray solitons. The results show that the gray soliton can be compressed by choosing the appropriate initial chirp, and the chirped gray pulses can stably propagate along optical fibers remaining the character of solitons.     

Noncontinuous Solitary Wave Solutions for Double sine-Gordon Equation

Using the tanh method and a variable separated ordinary difference equation method to solve the double sineGordon equation, we derive some new exact travelling wave solutions, especially a new type of noncontinuous solitary wave solutions. These noncontinuous solitary wave solutions are verified by using the conservation law theory.     

Switching and Self-trapping Dynamics of Dark Solitons in a Two-Component Bose-Einstein Condensate

Two coupled dark solitons are considered in a two-component Bose-Einstein condensate, and their dynamics are investigated by the variational approach based the renormalized integrals of motion. The stationary states as physical solutions to the describing equations are obtained, and the dynamic mechanism is demonstrated by performing a coordinate of a classical particle moving in an effective potential field. The switching and selftrapping dynamics of the coupled dark vector solitons are discussed by the evolution of the atom population transferring ratio.     

Grammian solutions and Pfaffianization of the non-isospectral modified Kadomtsev-Petviashvili equation

The Grammian determinant solutions of the non-isospectral modified Kadomtsev-Petviashvili (mKP) equation are presented. Moreover, a new non-isospectral coupled system is constructed by using the Pfaffianization procedure. Furthermore, Gramm-type Pfaffian solutions of the non-isospectral coupled system are obtained.     

Modulational instability and spatial structures of the Ablowitz-Ladik equation

Spatial structures as a result of a modulational instability are obtained in the integrable discrete nonlinear Schrödinger equation (Ablowitz-Ladik equation). Discrete slow space variables are used in a general setting and the related finite differences are constructed. Analyzing the ensuing equation, we derive the modulational instability criterion from the discrete multiple scales approach. Numerical simulations in agreement with analytical studies lead to the disintegrations of the initial modulated waves into a train of pulses.