Abstract
In this paper, we seek connections between the Sylvester equation and the Ablowitz—Kaup—Newell—Segur (AKNS) system. By the Sylvester equation KM — MK = r sT, we introduce master function S(i, j) = sT Kj (I + M)−1Kir. This function satisfies some recurrence relations. By imposing dispersion relations on r and s, we study the constructions of the AKNS system, where some AKNS type equations are investigated emphatically, including second-AKNS equation, second-modified AKNS (mAKNS) equation, third-AKNS equation, third-mAKNS equation and (—1)st-AKNS equation. The reductions of these equations to complex Korteweg—de Vries (KdV) equation, real and complex modified Korteweg—de Vries (mKdV) type equations, nonlinear Schrodinger (NLS) type equations and sine-Gordon (sG) equation are discussed.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
