Hamiltonian form of extended cubic-quintic nonlinear Schrödinger equation in a nonlinear Klein-Gordon model

具有周期势的五阶非线性薛定谔方程中暗孤子的存在性

On existence of dark solitons in cubic-quintic nonlinear Schrödinger equation with a periodic potential

证明了具有周期势的五阶非线性薛定谔方程的稳态暗孤子解的存在性.它是基于解释的暗孤子作为一个异宿的庞加莱映射。

Variational Approximations of Bifurcations of Asymmetric Solitons in Cubic-Quintic Nonlinear Schroedinger Lattices

Using a variational approximation we study discrete solitons of a nonlinear Schroedinger lattice with a cubic-quintic nonlinearity. Using an ansatz with six parameters we are able to approximate bifurcations of asymmetric solutions connecting site-centered and bond-centered solutions and resulting in the exchange of their stability. We show that the numerically exact and variational approximations are quite close for solitons of small powers.

Bistability and instability of dark-antidark solitons in the cubic-quintic nonlinear Schroedinger equation

We characterize the full family of soliton solutions sitting over a background plane wave and ruled by the cubic-quintic nonlinear Schroedinger equation in the regime where a quintic focusing term represents a saturation of the cubic defocusing nonlinearity. We discuss existence and properties of solitons in terms of catastrophe theory and fully characterize bistability and instabilities of the dark-antidark pairs, revealing new mechanisms of decay of antidark solitons.

Propagating Wave Patterns in a Derivative Nonlinear Schrödinger System with Quintic Nonlinearity

Exact expressions are obtained for a diversity of propagating patterns for a derivative nonlinear Schrödinger equation with a quintic nonlinearity. These patterns include bright pulses, fronts and dark solitons. The evolution of the wave envelope is determined via a pair of integrals of motion, and reduction is achieved to Jacobi elliptic cn and dn function representations. Numerical simulations are performed to establish the existence of parameter ranges for stability. The derivative quintic nonlinear Schrödinger model equations investigated here are important in the analysis of strong optica…

Mapping Between Generalized Nonlinear Schroedinger Equations and Neutral Scalar Field Theories and New Solutions of the Cubic-Quintic NLS Equation

We highlight an interesting mapping between the moving breather solutions of the generalized Nonlinear Schrodinger (NLS) equations and the static solutions of neutral scalar field theories. Using this connection, we then obtain several new moving breather solutions of the cubic-quintic NLS equation both with and without uniform phase in space. The stability of some stationary solutions is investigated numerically and the results confirmed via dynamical evolution.

Nonlinear compression of autonomous similaritons in the cubic-quintic nonlinear Schrödinger equation model with nonlinear gain

We describe similariton pulse propagation in double-doped optical fibers with the aid of self-similarity analysis of the cubic-quintic nonlinear Schrödinger equation with varying dispersion, nonlinearity, gain or absorption, and nonlinear gain. Exact similariton pulses that can propagate self similarly subject to simple scaling rules of this model have been found using a fractional transform. By appropriately tailoring the dispersion profile and nonlinearity, the condition for optimal pulse compression has been obtained. Also, nonlinear chirping of the trigonometric solution has been demonstra…

One-dimensional gap solitons in quintic and cubic-quintic Fractional nonlinear Schrödinger equations with a periodically modulated linear potential

Competing nonlinearities, such as the cubic (Kerr) and quintic nonlinear terms whose strengths are of opposite signs (the coefficients in front of the nonlinearities), exist in various physical media (in particular, in optical and matter-wave media). A benign competition between self-focusing cubic and self-defocusing quintic nonlinear nonlinearities (known as cubic-quintic model) plays an important role in creating and stabilizing the self-trapping of D-dimensional localized structures, in the contexts of standard nonlinear Schrödinger equation. We incorporate an external periodic potential (…

三次-五次非线性薛定谔方程中双稳态孤子的量子涨落

Quantum Fluctuations around Bistable Solitons in the Cubic-Quintic nonlinear Schrödinger equation

在线性近似下，研究了五阶非线性薛定谔方程（CQNLSE）描述的孤子中的小量子涨落。考虑了自散焦和自聚焦五次项的情况（在后一种情况下，孤子可能是有效稳定的，尽管有崩溃的可能性）。数值实现的反向传播方法被用来计算量子涨落与传输距离的最佳压缩比。在自散焦五次非线性情况下，三次项和五次项前面的符号相反，使得在相同宽度下具有不同能量的两个孤子对周围的涨落完全不同。研究了CQNLSE模型中非平稳高斯脉冲周围的涨落。

五阶非线性薛定谔方程自旋环孤子的稳定性

Stability of spinning ring solitons of the cubic-quintic nonlinear Schrodinger equation

研究了具有聚焦立方和散焦五次非线性项的非线性薛定谔方程的（2+1）维环孤子的稳定性。计算特征值的线性方程，我们表明，环自旋（拓扑电荷）S=1和S=2是线性稳定的，只要它们是非常广泛的。稳定区域分别占相应存在区域的9%和8%。这些结果最终解决了这类模型的一个有争议的稳定性问题。