Master-Thesis: Backlund Transformation for Certain Series of the Matrix Constrained Kadomtsev-Petviashvili Hierarchy

The Kadomtsev-Petviashvili (KP) hierarchy is a classic integrable system, and the study of the KP hierarchy has always been an important topic in the development of the soliton theory. In this research, we study a special invariant submanifold of the KP hierarchy from the perspective of Lie algebra. The induced hierarchy is called the Matrix restricted modified constrained KP (Matrix rmcKP) hierarchy. Then, through the factorization theory of the loop group, we construct the Backlund Transformation (BT) for the Matrix rmcKP hierarchy. As an example. we apply the BT to the complex-value (imaginary-value) modified KdV equation to obtain the explicit solutions.

The initial_version is in English.

The final version 18215015_Ziyu She.pdf is in Chinese.

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