Matrix Korteweg-de Vries and modified Korteweg-de Vries hierarchies: Noncommutative soliton solutions

Abstract

The present work continues work on KdV-type hierarchies presented by S. Carillo and C. Schiebold [“Noncommutative Korteweg-de Vries and modified Korteweg-de Vries hierarchies via recursion methods,” J. Math. Phys. 50, 073510 (2009)]10.1063/1.3155080. General solution formulas for the KdV and mKdV hierarchies are derived by means of Banach space techniques both in the scalar and matrix case. A detailed analysis is given of solitons, breathers, their countable superpositions as well as of multisoliton solutions for the matrix hierarchies.