Quaternion algebra approach to nonlinear Schrödinger equations with nonvanishing boundary conditions

Francesco Demontis
;Cornelis van der Mee
2023-01-01

Abstract

In this article we apply quaternionic linear algebra and quaternionic linear system theory to develop the inverse scattering transform theory for the nonlinear Schrödinger equation with nonvanishing boundary conditions. We also determine its soliton solutions by using triplets of quaternionic matrices.
2023
Miura transformation; Matrix KdV equation; Focusing NLS equation; Matrix triplet method; Quaternionic scattering theory
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