Dynamics of the smooth positons of the reverse space-time nonlocal Fokas-Lenells equation

Abstract In this paper, based on the determinant representation of the $n$-order soliton solutions, static soliton solution can be obtained by assigning different values of eigenvalues. Under the premise of the degenerate Darboux transformation (DT), the determinant representation of the $n$-order positon solutions and breather-positon solutions of the reverse space-time (RST) nonlocal Fokas–Lenells (FL) equation are obtained by performing a high-order Taylor expansion on the eigenvalues under the special limits $ \lambda_{2j-1} \to \lambda_1, \lambda_{2j} \to \lambda_2,$ with $\lambda_2=\lambda_1^* (j=2,3,...,n)$. In summary, three kinds \textcolor{black}{of} positon solutions and two breather-positon solutions can be derived. Additionally, the exact solution of the $2$-positon solution is produced. Furthermore, three kinds of mixed solutions are also presented, namely the $1$-soliton $2$-positon, $2$-soliton $2$-positon and $1$-soliton $3$-positon solutions. It is clearly demonstrated that these solutions possess new properties distinct from those of soliton solutions. Finally, the interaction properties between positons and solitons are investigated in detail.