标题： 一般双分量长波短波共振相互作用系统：非退化矢量孤子及其碰撞动力学 显示英文标题

标题： General two-component long-wave short-wave resonance interaction system: Non-degenerate vector solitons and their collision dynamics

摘要： 在本文中，我们展示了非退化亮孤子的出现，并总结了它们在一个完全可积的两成分长波短波共振相互作用模型中的几个有趣特征，该模型具有非线性系数的一般形式。 通过经典的hirota双线性方法，我们为这个LSRI模型获得了全非退化的$N$孤子解，以gram行列式形式表示。 根据速度条件的选择，所获得的非退化基本孤子被分类为两种类型，即($1,1,1$)和($1,1,2$)非退化单孤子。 然后我们展示基本($1,1,1$)非退化孤子表现出新的轮廓结构，包括双峰、特殊平顶和常规单峰轮廓，而($1,1,2$)非退化孤子允许类似于KP线孤子与短茎结构相互作用的倾斜碰撞行为。 进行了详细的渐近分析以研究($1,1,1$)非退化孤子的长时间行为，结果显示它们经历了形状保持和形状变化的碰撞。 然而，我们的分析确认这些孤子之间的形状变化碰撞在时间坐标适当偏移后变得具有弹性。 此外，我们确定($1,1,2$)非退化孤子也经历弹性碰撞。 此外，我们还研究了在退化孤子与非退化孤子（$1,1,1$）碰撞过程中呼吸现象的形成或抑制。 为了完整性，我们还指出了完全退化孤子之间的碰撞情形。 本文中提出的结果广泛适用于玻色-爱因斯坦凝聚体、非线性光学、等离子体物理以及其他相关领域。 显示英文摘要

摘要： In this paper, we demonstrate the emergence of non-degenerate bright solitons and summarize their several interesting features in a completely integrable two-component long-wave-short-wave resonance interaction model with a general form of nonlinearity coefficients. Through the classical Hirota's bilinear method, we obtain a fully non-degenerate $N$-soliton solution in Gram determinant form for this LSRI model. Depending on the choice of velocity conditions, the obtained non-degenerate fundamental soliton is classified into two types, namely ($1,1,1$)- and ($1,1,2$)-non-degenerate one solitons. We then show that the basic ($1,1,1$)-non-degenerate soliton exhibits novel profile structures, including a double-hump, a special flat-top, and a conventional single-hump profile, and ($1,1,2$)-non-degenerate soliton admits two-soliton like oblique collision, a behavior akin to KP line soliton interaction with a short stem structure. A detailed asymptotic analysis is carried out to study the long time behavior of ($1,1,1$)-non-degenerate solitons and it reveals that they undergo both shape-preserving and shape-changing collisions. However, our analysis confirms that the shape changing collision between these solitons become elastic in nature after appropriate shift of time coordinates. Further, we identified that the ($1,1,2$)-non-degenerate solitons also undergo elastic collision. In addition, we have also investigated the formation or suppression of breathing phenomena during collision between a degenerate soliton and a ($1,1,1$)-non-degenerate soliton. For completeness, we also point out the collision scenario between the completely degenerate solitons. The results presented in this paper are broadly applicable to Bose-Einstein condensates, nonlinear optics, plasma physics, and other closely related fields.