Inverse scattering transform for a new non-isospectral integrable non-linear AKNS model

• Main Authors: Gao Xudong, Zhang Sheng
• Format: Article
• Language: English
• Published: VINCA Institute of Nuclear Sciences 2017-01-01
• Series: Thermal Science
• Subjects: non-isospectral integrable non-linear AKNS model; AKNS linear problem; Lax integrability; inverse scattering transformation method; soliton solution
• Online Access: http://www.doiserbia.nb.rs/img/doi/0354-9836/2017/0354-983617153G .pdf

Constructing integrable systems and solving non-linear partial differential equations are important and interesting in non-linear science. In this paper, Ablowitz-Kaup-Newell-Segur (AKNS)’s linear isospectral problem and its accompanied time evolution equation are first generalized by embedding a new non-isospectral parameter whose varying with time obeys an arbitrary smooth enough function of the spectral parameter. Based on the generalized AKNS linear problem and its evolution equation, a new non-isospectral Lax integrable non-linear AKNS model is then derived. Furthermore, exact solutions of the derived AKNS model is obtained by extending the inverse scattering transformation method with new time-varying spectral parameter. In the case of reflectinless potentials, explicit n-soliton solutions are finally formulated through the obtained exact solutions.