Soliton Solutions to Sasa–Satsuma-Type Modified Korteweg–De Vries Equations by Binary Darboux Transformations

Abstract

Sasa–Satsuma (SS)-type integrable matrix modified Korteweg–de Vries (mKdV) equations are derived from two group constraints, involving the replacement of the spectral matrix in the Ablowitz–Kaup–Newell–Segur matrix eigenproblems with its matrix transpose and its Hermitian transpose. Using the Lax pairs and dual Lax pairs of matrix eigenproblems as a foundation, binary Darboux transformations are constructed. These transformations, initiated with a zero seed solution, facilitate the generation of soliton solutions for the SS-type integrable matrix mKdV equations presented.

Keywords

• soliton hierarchy
• lax pair
• group constraints
• darboux transformations
• soliton solutions