April 4, 2024

A vector complex modified Korteweg-de Vries equation and its reduction

By using Hirota’s bilinear and Kadomtsev–Petviashvili (KP) reduction approaches, a vector complex modified Kordeweg-de Vries (vcmKdV) equation is studied systematically. We find out that the vcmKdV equation of 2-, 3-, 4- component can be reduced to Sasa-Satsuma, Sasa-Satsuma-mKdV, coupled Sasa- Satsuma equations, respectively. We first derive the bright and dark soliton solutions via a series of reduction procedures including dimension reduction and complex conjugate reduction. 

By further imposing conditions on the solutions to the vcmKdV equation, the soliton solutions for the Sasa-Satsuma, Sasa-Satsuma-mKdV and coupled Sasa- Satsuma equation are derived and are expected to find their physical applications. The explicit forms of one- and two-bright and dark soliton solutions are presented, and their asymptotic behavior are analyzed. It is quite interesting that the bright soliton can be classified into one-hump, two-hump and oscillated types while the dark soliton composes of regular dark, anti-dark, double hole, Mexican hat and anti-Mexican hat types.

About the speaker

Mr. Changyan Shi is a masters student attending the University of Texas Rio Grande Valley from the School of Mathematical and Statistical Sciences.