耦合Sasa-Satsuma方程的Darboux-穿衣变换和半有理解  

Darboux-dressing Transformation and Semirational Solution to the Coupled Sasa-Satsuma Equation

作　　者：王秀彬 田守富 WANG XIUBIN;TIAN SHOUFU(School of Mathematics,China University of Mining and Technology,Xuzhou 221116,China)

机构地区：[1]中国矿业大学数学学院,徐州221116

出　　处：《应用数学学报》2024年第1期124-138,共15页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金项目(批准号:12201622,11975306和12371255);中央高校基本科研业务费专项资金资助(批准号:2023QN1090)。

摘　　要：本文主要研究可积的耦合Sasa-Satsuma方程,它可用于描述两个超短脉冲在双折射或双模光纤中的传输动力学.通过Darboux-穿衣变换,可以得到一类半有理解.这类解能够展示出怪波与呼吸波之间各种有趣的叠加场景.这些结果将有助于丰富和解释出现在光纤和色散介质中一些相关的非线性现象.Under investigation in this work is the integrable coupled Sasa-Satsuma equation,which can be used to describe the propagation dynamics of two ultrashort pulses in the birefringent or two-mode fiber.Through the Darboux-dressing transformation,we obtain a family of semirational solutions.This family of solutions exhibits various scenes of superimposition between rogue waves and breathers.These results may contribute to enriching and explaining some related nonlinear phenomena in optical fibers and dispersive media.

关 键 词：可积系统 耦合Sasa-Satsuma方程 Darboux-穿衣变换 半有理解 

分 类 号：O175.24[理学—数学]