Tamilselvan K, Kanna T, Govindarajan A
Nonlinear Waves Research Lab, PG and Research Department of Physics, Bishop Heber College, Tiruchirappalli 620 017, Tamil Nadu, India.
Centre for Nonlinear Dynamics, School of Physics, Bharathidasan University, Tiruchirappalli 620 024, Tamil Nadu, India.
Chaos. 2019 Jun;29(6):063121. doi: 10.1063/1.5096844.
We study the formation and propagation of chirped elliptic and solitary waves in the cubic-quintic nonlinear Helmholtz equation. This system describes nonparaxial pulse propagation in a planar waveguide with Kerr-like and quintic nonlinearities along with spatial dispersion originating from the nonparaxial effect that becomes dominant when the conventional slowly varying envelope approximation fails. We first carry out the modulational instability (MI) analysis of a plane wave in this system by employing the linear stability analysis and investigate the influence of different physical parameters on the MI gain spectra. In particular, we show that the nonparaxial parameter suppresses the conventional MI gain spectrum and also leads to a nontrivial monotonic increase in the gain spectrum near the tails of the conventional MI band, a qualitatively distinct behavior from the standard nonlinear Schrödinger system. We then study the MI dynamics by direct numerical simulations, which demonstrate the production of ultrashort nonparaxial pulse trains with internal oscillations and slight distortions at the wings. Following the MI dynamics, we obtain exact elliptic and solitary wave solutions using the integration method by considering physically interesting chirped traveling wave ansatz. In particular, we show that the system features intriguing chirped antidark, bright, gray, and dark solitary waves depending upon the nature of nonlinearities. We also show that the chirping is inversely proportional to the intensity of the optical wave. In particular, the bright and dark solitary waves exhibit unusual chirping behavior, which will have applications in the nonlinear pulse compression process.
我们研究了立方-五次非线性亥姆霍兹方程中啁啾椭圆波和孤立波的形成与传播。该系统描述了在具有克尔型和五次非线性以及源于非傍轴效应的空间色散的平面波导中的非傍轴脉冲传播，当传统的慢变包络近似失效时，非傍轴效应变得占主导地位。我们首先通过线性稳定性分析对该系统中的平面波进行调制不稳定性（MI）分析，并研究不同物理参数对MI增益谱的影响。特别地，我们表明非傍轴参数抑制了传统的MI增益谱，并且还导致在传统MI带尾部附近的增益谱出现非平凡的单调增加，这与标准非线性薛定谔系统在性质上有明显不同的行为。然后我们通过直接数值模拟研究MI动力学，模拟结果展示了具有内部振荡且在波翼处有轻微畸变的超短非傍轴脉冲串的产生。在跟踪MI动力学之后，我们通过考虑物理上有趣的啁啾行波假设，使用积分方法获得了精确的椭圆波和孤立波解。特别地，我们表明该系统根据非线性的性质具有有趣的啁啾反暗、亮、灰和暗孤立波。我们还表明啁啾与光波强度成反比。特别地，亮孤立波和暗孤立波表现出不寻常的啁啾行为，这将在非线性脉冲压缩过程中有应用。
