耦合亥姆霍兹方程：啁啾孤立波
Coupled Helmholtz Equations : Chirped Solitary Waves
摘要：
在耦合三次非线性Helmholtz方程的框架下，研究了自陡和自频移条件下啁啾灰孤立波和反暗孤立波的存在性和稳定性.我们表明，对于自陡峭和自频移的特定组合，不仅存在啁啾，而且存在啁啾反转。具体而言，相关的非平凡相位具有两个强度依赖项，一个随着强度的倒数而变化，而另一个依赖于非克尔非线性，与强度成正比。这导致啁啾反转横跨孤波轮廓。研究了非傍轴参数对孤立波强度、速度和脉宽等物理量的影响。研究发现，通过改变非傍轴参数，可以调节孤立波的速度。这些非傍轴孤立波的稳定传播是通过适当的参数选择实现的。
英文摘要：
We investigate the existence and stability properties of the chirped gray and anti-dark solitary waves within the framework of coupled cubic nonlinear Helmholtz equation in the presence of self steepening and self frequency shift. We show that for a particular combination of the self steepening and the self frequency shift, there is not only chirping but also chirp reversal. Specifically, the associated nontrivial phase has two intensity dependent terms, one varies as the reciprocal of the intensity while the other, which depends on non-Kerr nonlinearities, is directly proportional to the intensity. This causes chirp reversal across the solitary wave profile. A different combination of non-Kerr terms leads to chirping but no chirp reversal.The influence of nonparaxial parameter on physical quantities such as intensity, speed and pulse-width of the solitary waves is studied too. It is found that the speed of the solitary waves can be tuned by altering the nonparaxial parameter. Stable propagation of these nonparaxial solitary waves is achieved by an appropriate choice of parameters.
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