Manakov系统的无色散极限、其Riemann不变量及其反向传播平面波的调制稳定性
On the dispersionless limit of the Manakov system, its Riemann invariants, and the modulational stability of its counterpropagating plane waves
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中文总结 AI 辅助
本文推导Manakov系统的无色散极限，得到Manakov-Whitham系统，证明其可积性，利用谱曲线分支点识别Riemann不变量，分类平面波调制稳定性，并通过数值模拟验证预测。
中文摘要 AI 辅助
我们研究了Manakov系统的无色散极限，该系统是非线性薛定谔方程的可积双分量推广。我们推导出所得的四分量属零Manakov-Whitham系统，刻画了其流体动力学结构，并证明其通过Haantjes张量检验的可积性。我们证明了与Manakov系统平面波解相关联的谱曲线的分支点是无色散系统的局部Riemann不变量。我们还利用特征速度对平面波的基带调制稳定性/不稳定性进行分类，并研究了Manakov系统的直接线性化以刻画其有限波数稳定性，并验证在长波极限下与Whitham预测的一致性。最后，我们通过将预测与直接数值模拟结果进行比较来验证这些预测。
英文摘要
We study the dispersionless limit of the Manakov system, the integrable two-component generalization of the nonlinear Schrödinger equation. We derive the resulting four-component genus-zero Manakov-Whitham system, characterize its hydrodynamic structure, and show that it passes the Haantjes tensor test for integrability. We show that the branch points of the spectral curve associated with plane wave solutions of the Manakov system are the local Riemann invariants of the dispersionless system. We also use the characteristic speeds to classify the baseband modulational stability/instability of the plane waves, and we study a direct linearization of the Manakov system to characterize their finite-wavenumber stability and verify agreement with the Whitham prediction in the long-wave limit. Finally, we validate the predictions by comparing them with the results of direct numerical simulations.
