Breathers and localized solutions of complex modified Korteweg–de Vries equation

Abstract

Under investigation is the complex modified Korteweg–de Vries (KdV) equation, which has many physical significance in fluid mechanics, plasma physics and so on. Via the Darboux transformation (DT) method, some breather and localized solutions are presented on two backgrounds: the continuous wave background [Formula: see text] and the constant background [Formula: see text]. Some figures are plotted to illustrate the dynamical features of those solutions.