The vector form of Kundu-Eckhaus equation and its simplest solutions

Abstract

In our work a hierarchy of integrable vector nonlinear differential equations depending on the functional parameter $r$ is constructed using a monodromy matrix. The first equation of this hierarchy for $r=α(\mathbf{p}^t\mathbf{q})$ is vector analogue of the Kundu-Eckhaus equation. When $α=0$, the equations of this hierarchy turn into equations of the Manakov system hierarchy. New elliptic solutions to vector analogue of the Kundu-Eckhaus and Manakov system are presented. In conclusion, it is shown that there exist linear transformations of solutions to vector integrable nonlinear equations into other solutions to the same equations.

Figures (3)

• Figure 1: Magnitudes of solutions \ref{['sol.1']} for $k=0.7$, $c_1=1$
• Figure 2: Magnitudes of solutions \ref{['sol.4']} for $a=1$, $k_1=2$, $k_2=3$, $c_1=1$.
• Figure 3: Magnitudes of solutions \ref{['sol.g2']} for $a=3$, $b=5$, $c_1=1$, $t_a=2$, $t_b=3$.