On construction and integrability of the noncommutative extended KP equation and the noncommutative extended mKP equation

Abstract: Generalization of soliton theory and integrable systems to their noncommutative counterparts is an interesting topic. Some classical integrable systems have been generalized to their noncommutative versions and their integrability has been investigated. Moreover, as is known that integrable systems are closely related to other topcis such as orthogonal polynomials and combinatorics. Their noncommutative generalization is of great research interest too. KP equation is one of the most fundamental among many soliton equations. Its generalizations and extensions have been paid much attention to. In this talk, I will talk about how to construct the noncommutative extended KP equation and the noncommutative extended modified KP equation by using variation of parameter. As a consequence, two types of quasideterminant solutions are presented for the two noncommutative extended integrable systems respectively. In addition, Miura transformations between them are established successfully as well.

mathematical physics

Audience: researchers in the topic

Seminar-Type Workshop on Noncommutative Integrable Systems