Abstract
In this work, we use the inverse scattering transform method to consider the focusing Kundu–Eckhaus (KE) equation with nonzero background (NZBG) at infinity. Based on the analytical, symmetric, asymptotic properties of eigenfunctions, the inverse problem is solved via a matrix Riemann–Hilbert problem (RHP). The general multi-pole solutions are given in terms of the solution of the associated RHP. And the formula of the N simple-pole soliton solutions are obtained, too. We show that the Peregrine’s rational solution can be viewed as some appropriate limit of the simple-pole soliton solutions at branch point. Furthermore, by taking some other proper limits, the two and three simple-pole soliton solutions can yield to the double- and triple-pole solutions for focusing KE equation with NZBG. The effect of the parameter $$\beta $$ , characterizing the strength of the non-Kerr (quintic) nonlinear and the self-frequency shift effect, and some typical collisions between solutions of focusing KE equation are graphically displayed.
Sign-in/Register to access full text options 
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.
