研究目的
To explore the coupled derivative nonlinear Schr?dinger (DNLS) equation systematically by giving its infinitely many conservation laws, discussing the modulation instability of the plane wave solutions, and constructing higher-order semirational solutions.
研究成果
The study systematically explores the coupled DNLS equation by deriving its conservation laws, analyzing modulation instability, and constructing higher-order semirational solutions. The solutions are classified into three types, providing insights into the dynamics of nonlinear waves in the system.
研究不足
The study is theoretical and focuses on mathematical derivations and solutions of the coupled DNLS equation. The practical implementation and experimental validation of the solutions are not discussed.
1：Experimental Design and Method Selection:
The study employs the Darboux transformation method and utilizes particular vector solutions of the Lax pair to construct solutions for the coupled DNLS equation.
2：Sample Selection and Data Sources:
The study focuses on the coupled DNLS equation and its solutions, without external data sources.
3：List of Experimental Equipment and Materials:
The research is theoretical and does not involve physical equipment or materials.
4：Experimental Procedures and Operational Workflow:
The methodology involves constructing the Lax pair, deriving conservation laws, analyzing modulation instability, and applying the Darboux transformation to derive semirational solutions.
5：Data Analysis Methods:
The analysis is based on mathematical derivations and symbolic computations to explore the dynamics of the solutions.
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