Abstract
AbstractIn 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.
Funder
Università degli Studi di Cagliari
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,General Mathematics
Reference41 articles.
1. Ablowitz, M. J.: Nonlinear Dispersive Waves. Asymptotic Analysis and Solitons, Cambridge Texts in Applied Mathematics 47, Cambridge University Press, Cambridge (2011)
2. Ablowitz, M.J., Segur, H.: Solitons and Inverse Scattering Transforms. SIAM, Philadelphia (1981)
3. Agranovich, Z.S., Marchenko, V.A.: The Inverse Problem of Scattering Theory, Gordon and Breach, New York, 1963; also: Dover Publ., New York (2020)
4. Aktosun, T., Klaus, M., van der Mee, C.: Small-energy asymptotics of the scattering matrix for the matrix Schrödinger equation on the line. J. Math. Phys. 42, 4627–4652 (2001)
5. Aktosun, T., Weder, R.: Inverse scattering on the half line for the matrix Schrödinger equation. J. Math. Phys. Anal. Geom. 14, 237–269 (2018)