标题： 退化孤子解及其在耦合Hirota方程中的相互作用，具有平凡和非平凡背景 显示英文标题

标题： Degenerate soliton solutions and their interactions in coupled Hirota equation with trivial and nontrivial background

摘要： 我们构造了两种退化孤子解，一种是在零背景下的解，另一种是在平面波背景下的解，针对耦合的Hirota方程。 在零背景场的情况下，我们推导出不同阶数的正定解。 我们还通过渐近分析研究了正定解之间的相互作用动力学，并表明正定解在碰撞过程中表现出时间依赖的相位变化。 我们还构造了由正定解和孤子组成的混合解，并详细研究了高阶正定解与多孤子之间的相互作用。 从相互作用中，我们展示了多孤子和高阶正定解之间发生弹性和非弹性相互作用。 此外，我们为耦合的Hirota方程构造了孤子和正定解之间的束缚态。 在平面波背景的情况下，我们构造了呼吸子-正定解。 对于耦合的Hirota方程，呼吸子-正定解首次在文献中被报道。 从呼吸子-正定解中，我们揭示了呼吸子-正定解与正定解之间的一些有趣的碰撞动力学。 显示英文摘要

摘要： We construct two kinds of degenerate soliton solutions, one on the zero background and another on the plane wave background for the coupled Hirota equation. In the case of zero background field, we derive positon solutions of various orders. We also study interaction dynamics between positon solutions through asymptotic analysis and show that the positons exhibit time dependent phase shift during collision. We also construct hybrid solutions which composed of positons and solitons and examine the interaction between higher order positon and multi-solitons in detail. From the interaction, we demonstrate that the occurrence of elastic and inelastic interaction between multi-solitons and higher order positons. Further, we construct bound states among solitons and positons for the coupled Hirota equation. In the case of plane wave background, we construct breather-positon solutions. For the coupled Hirota equation, the breather-positon solutions are being reported first time in the literature. From the breather-positon solutions, we bring out certain interesting collision dynamics between breather-positons and positons.