2016•Journal of Physics Conference SeriesOpen access

Soliton solutions of the (2+1)-dimensional complex modified Korteweg-de Vries and Maxwell-Bloch equations

Kuralay Yesmakhanova, Guldana Bekova, Gaukhar Shaikhova, Ratbay Myrzakulov

Abstract

In this paper, we consider the (2+1)-dimensional complex modified Korteweg-de Vries and Maxwell-Bloch (cmKdVMB) equations. Lax pairs of cmKdVMB equations are presented. Using the Lax pair, we construct a Darboux transformation and namely one-fold transformations. The soliton solutions are obtained from the different "seeds" by using this Darboux transformation.

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Key concepts: Lax pair, Soliton, Transformation (genetics), Mathematical physics, Korteweg–de Vries equation, Mathematics, Maxwell's equations, Bloch equations