Gromov Evgeny, Malomed Boris
Higher School of Economics, National Research University, Nizhny Novgorod 603155, Russia.
Department of Physical Electronics, School of Electrical Engineering, Faculty of Engineering, and Center for Light-Matter Interaction, Tel Aviv University, Tel Aviv 69978, Israel.
Chaos. 2017 Nov;27(11):113107. doi: 10.1063/1.5000923.
New two-component soliton solutions of the coupled high-frequency (HF)-low-frequency (LF) system, based on Schrödinger-Korteweg-de Vries (KdV) system with the Zakharov's coupling, are obtained for arbitrary relative strengths of the nonlinearity and dispersion in the LF component. The complex HF field is governed by the linear Schrödinger equation with a potential generated by the real LF component, which, in turn, is governed by the KdV equation including the ponderomotive coupling term, representing the feedback of the HF field onto the LF component. First, we study the evolution of pulse-shaped pulses by means of direct simulations. In the case when the dispersion of the LF component is weak in comparison to its nonlinearity, the input gives rise to several solitons in which the HF component is much broader than its LF counterpart. In the opposite case, the system creates a single soliton with approximately equal widths of both components. Collisions between stable solitons are studied too, with a conclusion that the collisions are inelastic, with a greater soliton getting still stronger, and the smaller one suffering further attenuation. Robust intrinsic modes are excited in the colliding solitons. A new family of approximate analytical two-component soliton solutions with two free parameters is found for an arbitrary relative strength of the nonlinearity and dispersion of the LF component, assuming weak feedback of the HF field onto the LF component. Further, a one-parameter (non-generic) family of exact bright-soliton solutions, with mutually proportional HF and LF components, is produced too. Intrinsic dynamics of the two-component solitons, induced by a shift of their HF component against the LF one, is also studied, by means of numerical simulations, demonstrating excitation of a robust intrinsic mode. In addition to the above-mentioned results for LF-dominated two-component solitons, which always run in one (positive) velocities, we produce HF-dominated soliton complexes, which travel in the opposite (negative) direction. They are obtained in a numerical form and by means of a quasi-adiabatic analytical approximation. The solutions with positive and negative velocities correspond, respectively, to super- and subsonic Davydov-Scott solitons.
基于具有扎哈罗夫耦合的薛定谔 - 科特韦格 - 德弗里斯（KdV）系统，针对低频分量中非线性和色散的任意相对强度，获得了耦合高频（HF） - 低频（LF）系统的新的双组分孤子解。复高频场由具有由实低频分量产生的势的线性薛定谔方程控制，而实低频分量又由包含 ponderomotive 耦合项的 KdV 方程控制，该耦合项表示高频场对低频分量的反馈。首先，我们通过直接模拟研究脉冲形状脉冲的演化。在低频分量的色散与其非线性相比很弱的情况下，输入会产生几个孤子，其中高频分量比其低频对应物宽得多。在相反的情况下，系统会产生一个单孤子，其两个分量的宽度近似相等。还研究了稳定孤子之间的碰撞，得出的结论是碰撞是非弹性的，较大的孤子变得更强，较小的孤子进一步衰减。在碰撞孤子中激发了稳健的本征模。对于低频分量中非线性和色散的任意相对强度，在假设高频场对低频分量的反馈较弱的情况下，找到了一个具有两个自由参数的新的近似解析双组分孤子解族。此外，还产生了一个单参数（非通用）的精确亮孤子解族，其高频和低频分量相互成比例。还通过数值模拟研究了双组分孤子由于其高频分量相对于低频分量的偏移而引起的本征动力学，证明了稳健本征模的激发。除了上述总是以一个（正）速度运行的低频主导的双组分孤子的结果外，我们还产生了以相反（负）方向传播的高频主导的孤子复合体。它们通过数值形式和准绝热解析近似获得。具有正速度和负速度的解分别对应于超音速和亚音速的达维多夫 - 斯科特孤子。
