Modulational instability and position controllable discrete rogue waves with interaction phenomena in the semi-discrete complex coupled dispersionless system

Some new soliton solutions of a semi-discrete fractional complex coupled dispersionless system

“…17 , the bright soliton solution, breather solution and rogue wave solution of the semi-discrete complex coupled dispersionless integrable system (SDCCD) are obtained using Lax pairs and Darboux transformation method. Also, the modulational instability of SDCCD is studied in 20 .…”

“…So, in this paper, we introduce the semi-discrete M-fractional derivative complex coupled dispersionless (FDSDCCD) system where q n = q(n, t) , R n = R(n, t) and R n+1 = R(n + 1, t) . The FDSDCCD system physically used for describing the interaction of current-fed string in a certain external magnetic field 20 .…”

Hybrid rogue waves and breather solutions on the double-periodic background for the Kundu-DNLS equation

“…A hybrid structure of solitons and breathers is constructed [28]. Extended DT has been used to study hybrid rogue waves and breather waves [29][30][31], which can describe the interaction between the current-fed string and the external magnetic field and other physical phenomena [32]. Therefore, it is very important to study hybrid rogue waves and breather waves.…”