Propagation and interaction of two-component vector dark solitons in the defocusing nonlinear media

Based on reduction of the KP hierarchy, the general multi-dark soliton solutions in Gram type determinant forms for the (2[Formula: see text]+[Formula: see text]1)-dimensional multi-component Maccari system are constructed. Especially, the two component coupled Maccari system comprising of two component short waves and single-component long waves are discussed in detail. Besides, the dynamics of one and two dark-dark solitons are analyzed. It is shown that the collisions of two dark-dark solitons are elastic by asymptotic analysis. Additionally, the two dark-dark solitons bound states are studied through two different cases (stationary and moving cases). The bound states can exist up to arbitrary order in the stationary case, however, only two-soliton bound state exists in the moving case. Besides, the oblique stationary bound state can be generated for all possible combinations of nonlinearity coefficients consisting of positive, negative and mixed cases. Nevertheless, the parallel stationary and the moving bound states are only possible when nonlinearity coefficients take opposite signs.

Download Full-text

A pair of modified short pulse equations and its two-component system in nonlinear media

Wave Motion ◽

10.1016/j.wavemoti.2020.102553 ◽

2020 ◽

Vol 96 ◽

pp. 102553

Author(s):

Zhaqilao

Keyword(s):

Short Pulse ◽

Two Component System ◽

Nonlinear Media ◽

Component System ◽

Two Component

Download Full-text

Dark gap solitons in periodic nonlinear media with competing cubic-quintic nonlinearities

10.21203/rs.3.rs-292763/v1 ◽

2021 ◽

Author(s):

Junbo Chen ◽

Jianhua Zeng

Keyword(s):

Wave Spectrum ◽

Bloch Wave ◽

Nonlinear Phenomenon ◽

Nonlinear Media ◽

Dark Solitons ◽

Periodic Potentials ◽

Stability And Instability ◽

Gap Solitons ◽

The Stability ◽

Finite Band

Abstract Solitons are nonlinear self-sustained wave excitations and probably among the most interesting and exciting emergent nonlinear phenomenon in the corresponding theoretical settings. Bright solitons with sharp peak and dark solitons with central notch have been well known and observed in various nonlinear systems. The interplay of periodic potentials, like photonic crystals and lattices in optics and optical lattices in ultracold atoms, with the dispersion has brought about gap solitons within the finite band gaps of the underlying linear Bloch-wave spectrum and, particularly, the bright gap solitons have been experimentally observed in these nonlinear periodic systems, while little is known about the underlying physics of dark gap solitons. Here, we theoretically and numerically investigate the existence, property and stability of one-dimensional gap solitons and soliton clusters in periodic nonlinear media with competing cubic-quintic nonlinearity, the higher-order of which is self-defocusing and the lower-order (cubic) one is chosen as self-defocusing or focusing nonlinearities. By means of the conventional linear-stability analysis and direct numerical calculations with initial perturbations, we identify the stability and instability areas of the corresponding dark gap solitons and clusters ones.

Download Full-text