Stalin S, Ramakrishnan R, Lakshmanan M
Department of Nonlinear Dynamics, Bharathidasan University, Tiruchirapalli-620 024, India.
Phys Rev E. 2022 Apr;105(4-1):044203. doi: 10.1103/PhysRevE.105.044203.
In this paper, we study the dynamics of an interesting class of vector solitons in the long-wave-short-wave resonance interaction (LSRI) system. The model that we consider here describes the nonlinear interaction of long wave and two short waves and it generically appears in several physical settings. To derive this class of nondegenerate vector soliton solutions we adopt the Hirota bilinear method with the more general form of admissible seed solutions with nonidentical distinct propagation constants. We express the resultant fundamental as well as multisoliton solutions in a compact way using Gram-determinants. The general fundamental vector soliton solution possesses several interesting properties. For instance, the double-hump or a single-hump profile structure including a special flattop profile form results in when the soliton propagates in all the components with identical velocities. Interestingly, in the case of nonidentical velocities, the soliton number is increased to two in the long-wave component, while a single-humped soliton propagates in the two short-wave components. We establish through a detailed analysis that the nondegenerate multisolitons in contrast to the already known vector solitons (with identical wave numbers) can undergo three types of elastic collision scenarios: (i) shape-preserving, (ii) shape-altering, and (iii) a shape-changing collision, depending on the choice of the soliton parameters. Here, by shape-altering we mean that the structure of the nondegenerate soliton gets modified slightly during the collision process, whereas if the changes occur appreciably then we call such a collision as shape-changing collision. We distinguish each of the collision scenarios, by deriving a zero phase shift criterion with the help of phase constants. Very importantly, the shape-changing behavior of the nondegenerate vector solitons is observed in the long-wave mode also, along with corresponding changes in the short-wave modes, and this nonlinear phenomenon has not been observed in the already known vector solitons. In addition, we point out the coexistence of nondegenerate and degenerate solitons simultaneously along with the associated physical consequences. We also indicate the physical realizations of these general vector solitons in nonlinear optics, hydrodynamics, and Bose-Einstein condensates. Our results are generic and they will be useful in these physical systems and other closely related systems including plasma physics when the long-wave-short-wave resonance interaction is taken into account.
在本文中，我们研究了长波-短波共振相互作用（LSRI）系统中一类有趣的矢量孤子的动力学。我们在此考虑的模型描述了长波与两个短波的非线性相互作用，并且它通常出现在多种物理情形中。为了推导这类非简并矢量孤子解，我们采用Hirota双线性方法以及具有不同传播常数的更一般形式的容许种子解。我们使用Gram行列式以紧凑的方式表示所得的基本孤子解以及多孤子解。一般的基本矢量孤子解具有几个有趣的性质。例如，当孤子在所有分量中以相同速度传播时，会产生双峰或单峰轮廓结构，包括一种特殊的平顶轮廓形式。有趣的是，在速度不同的情况下，长波分量中的孤子数增加到两个，而单峰孤子在两个短波分量中传播。通过详细分析我们确定，与已知的（具有相同波数的）矢量孤子相比，非简并多孤子可以经历三种类型的弹性碰撞情形：（i）形状保持型，（ii）形状改变型，以及（iii）形状变化型碰撞，这取决于孤子参数的选择。这里，形状改变是指非简并孤子的结构在碰撞过程中略有改变，而如果变化明显，则我们称这种碰撞为形状变化型碰撞。我们借助相位常数推导零相位偏移准则来区分每种碰撞情形。非常重要的是，在长波模式中也观察到了非简并矢量孤子的形状变化行为，同时短波模式也有相应变化，并且这种非线性现象在已知的矢量孤子中尚未观察到。此外，我们指出了非简并和简并孤子的同时共存以及相关的物理后果。我们还指出了这些一般矢量孤子在非线性光学、流体动力学和玻色-爱因斯坦凝聚体中的物理实现。我们的结果具有普遍性，当考虑长波-短波共振相互作用时，它们将在这些物理系统以及包括等离子体物理在内的其他密切相关系统中有用。
