Recently, we have shown that the Manakov equation can admit a more general class of nondegenerate vector solitons, which can undergo collision without any intensity redistribution in general among the modes, associated with distinct wave numbers, besides the already-known energy exchanging solitons corresponding to identical wave numbers. In the present comprehensive paper, we discuss in detail the various special features of the reported nondegenerate vector solitons. To bring out these details, we derive the exact forms of such vector one-, two-, and three-soliton solutions through Hirota bilinear method and they are rewritten in more compact forms using Gram determinants. The presence of distinct wave numbers allows the nondegenerate fundamental soliton to admit various profiles such as double-hump, flat-top, and single-hump structures. We explain the formation of double-hump structure in the fundamental soliton when the relative velocity of the two modes tends to zero. More critical analysis shows that the nondegenerate fundamental solitons can undergo shape-preserving as well as shape-altering collisions under appropriate conditions. The shape-changing collision occurs between the modes of nondegenerate solitons when the parameters are fixed suitably. Then we observe the coexistence of degenerate and nondegenerate solitons when the wave numbers are restricted appropriately in the obtained two-soliton solution. In such a situation we find the degenerate soliton induces shape-changing behavior of nondegenerate soliton during the collision process. By performing suitable asymptotic analysis we analyze the consequences that occur in each of the collision scenario. Finally, we point out that the previously known class of energy-exchanging vector bright solitons, with identical wave numbers, turns out to be a special case of nondegenerate solitons.

中文翻译：

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非退化孤子及其在Manakov系统中的碰撞

最近，我们证明了Manakov方程可以接受更一般的一类非退化矢量孤子，除了已知的与之对应的能量交换孤子，该孤子可以在没有任何强度重新分布的情况下发生碰撞，并且在各个模式之间通常不会发生任何强度重新分布。相同的波数。在当前的综合论文中，我们详细讨论了所报道的非简并矢量孤子的各种特殊特征。为了阐明这些细节，我们通过Hirota双线性方法推导了此类矢量一，二和三孤子解的精确形式，并使用Gram行列式将它们重写为更紧凑的形式。不同波数的存在使未退化的基本孤子可以接受各种轮廓，例如双峰，平顶和单峰结构。当两种模式的相对速度趋于零时，我们解释了基本孤子中双峰结构的形成。更严格的分析表明，在适当的条件下，未退化的基本孤子可能会发生形状保持和形状更改的碰撞。当参数适当固定时，非简并孤子模式之间会发生形变碰撞。然后，当在所获得的两孤子解中适当限制波数时，我们观察了简并孤子与非简并孤子的共存。在这种情况下，我们发现简并孤子在碰撞过程中引起了非简并孤子的形状改变行为。通过执行适当的渐近分析，我们分析了每种碰撞情况下发生的后果。最后，