Rogue wave, interaction solutions to the KMM system

• Published in: Journal of magnetism and magnetic materials Vol. 502; p. 166590
• Main Authors: Jin, Xin-Wei, Lin, Ji
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 15.05.2020; Elsevier BV
• Subjects: Consistent tanh expansion method; Damping; Damping effects; Exact solutions; Ferromagnetism; Instantons; Kraenkel-Manna-Merle system; Multipoles; Painlevé analysis; Rogue wave; Solitary waves; Wave propagation; Painlevé analysis; Damping effects; Consistent tanh expansion method; Kraenkel-Manna-Merle system; Rogue wave
• ISSN: 0304-8853; 1873-4766
• DOI: 10.1016/j.jmmm.2020.166590

•A coupled nonlinear ferromagnetic system is investigated.•Two series of analytic solutions are obtained via the CTE method.•Rogue wave and interaction solutions are constructed.•Exact solutions of the non-integrable damped-KMM system. In this paper, the consistent tanh expansion (CTE) method and the truncated Painlevé analysis are applied to the Kraenkel-Manna-Merle (KMM) system, which describes propagation of short wave in ferromagnets. Two series of analytic solutions of the original KMM system (free of damping effect) are obtained via the CTE method. The interaction solutions contain an arbitrary function, which provides a wide variety of choices to acquire new propagation structures. Particularly, the breather soliton, periodic oscillation soliton and multipole instanton are obtained. Furthermore, we obtain some exact solutions of the damped-KMM equation at the first time. On the other hand, a coupled equation containing quadri-linear form and tri-linear form for the original KMM system is obtained by the truncated Painlevé analysis, and the rogue wave solution and interaction solutions between rogue wave and multi-soliton for the KMM system are discussed.