School of Physics, Northwest University, Xi'an 710069, China.
Shaanxi Key Laboratory for Theoretical Physics Frontiers, Xi'an 710069, China.
Chaos. 2017 Aug;27(8):083120. doi: 10.1063/1.4999916.
We study superregular (SR) breathers (i.e., the quasi-Akhmediev breather collision with a certain phase shift) in a complex modified Korteweg-de Vries equation. We demonstrate that such SR waves can exhibit intriguing nonlinear structures, including the half-transition and full-suppression modes, which have no analogues in the standard nonlinear Schrödinger equation. In contrast to the standard SR breather formed by pairs of quasi-Akhmediev breathers, the half-transition mode describes a mix of quasi-Akhmediev and quasi-periodic waves, whereas the full-suppression mode shows a non-amplifying nonlinear dynamics of localized small perturbations associated with the vanishing growth rate of modulation instability. Interestingly, we show analytically and numerically that these different SR modes can be evolved from an identical localized small perturbation. In particular, our results demonstrate an excellent compatibility relation between SR modes and the linear stability analysis.
我们研究了复宗量修正 Korteweg-de Vries 方程中的超正则（SR）呼吸子（即具有一定相移的准阿哈梅德伊夫呼吸子碰撞）。我们证明了这种 SR 波可以表现出有趣的非线性结构，包括半跃迁和全抑制模式，这些模式在标准非线性薛定谔方程中没有类似的对应物。与由准阿哈梅德伊夫呼吸子对组成的标准 SR 呼吸子不同，半跃迁模式描述了准阿哈梅德伊夫波和准周期波的混合，而全抑制模式则显示出与调制不稳定性增长率消失相关的局域小扰动的非放大非线性动力学。有趣的是，我们通过解析和数值方法证明，这些不同的 SR 模式可以从一个相同的局域小扰动演化而来。特别地，我们的结果展示了 SR 模式与线性稳定性分析之间的极好兼容性关系。
