Darboux transformations for the multicomponent vector solitons and rogue waves of the multiple coupled Kundu–Eckhaus equations

• Published in: Wave motion 2022-09, Vol.114, p.103041, Article 103041
• Main Authors: Dafounansou, O., Mbah, D.C., Taussé Kamdoum, F.L., Kwato Njock, M.G.
• Format: Article
• Language: English
• Subjects: Darboux transformation; n-coupled KE-equations; Rogue waves; Vector solitons
• ISSN: 0165-2125; 1878-433X
• DOI: 10.1016/j.wavemoti.2022.103041

In this paper, we inspect some novel localized waves solutions for the n-coupled Kundu–Eckhaus (KE)-equations (n≥3). The Lax pair for the 3-coupled KE equations is constructed and generalized to the n-components KE equations. In this way, for any n∈N∗, we determine the (n+1)×(n+1) Darboux matrix and the explicit expressions of both one-soliton solutions and two-soliton solutions. Furthermore, we apply the Darboux-dressing transformation to the n-coupled KE equations with non-vanishing background. Based on this technique, we derive the rogue waves and solutions for the 3-coupled KE equations. An appropriate choice of parameters allows us to appreciate the dynamics of soliton solutions for high values of n: n=3,35,50, and the dynamics of the rogue waves interacting with breathers for n=3. •One and two-soliton solutions for any system of n-coupled KE equations are given.•The Darboux-dressing transformation of n-coupled KE equations is provided.•Novel Rogue waves solutions and new profiles are obtained for n=3.