General rogue wave solutions and their dynamics in the complex modified Korteweg–de Vries equation - Yan Zhu; Lijuan Qin; Zhiqiang Yang; Zhenting Chen; Zhenyun Qin; Gui Mu (Results in Physics, 2025)
By means of the Hirota bilinear method together with the Kadomtsev–Petviashvili hierarchy reduction technique, general higher-order rogue wave solutions of the complex modified Korteweg–de Vries equation are derived explicitly. These solutions are expressed succinctly in terms of Gram determinants whose matrix elements are Schur polynomials. It is found that the highest peak amplitude of Nth-order rogue waves turns out to be 2N+1 times its background amplitude. The Nth-order rogue wave solutions contain the N−1 irreducible complex parameters. By selecting different values of these free parameters, the rich dynamic behaviors of rogue wave solutions of the complex modified Korteweg–de Vries equation are discovered.