Systematic soliton shape modulation by engineering superposed plane wave and soliton parameters

We investigate the linear interference of a plane wave with different localized waves using the coupled Fokas-Lenells equation (FLE) with four-wave mixing term. We obtain the localized wave solution of the coupled FLE by linear superposition of two distinctly independent wave solutions, namely, the plane wave and one soliton solution and the plane wave and two soliton solution. We obtain several nonlinear profiles depending on the relative phase induced by soliton parameters. We present a systematic analysis of the linear interference profile under four different conditions on the spatial and temporal phase coefficients of interfering waves. We further investigate the interaction of two soliton solution and a plane wave. In this case, we find that, asymptotically, two soliton profiles may be similar or different from each other depending on the choices of soliton parameters in the two cases. The present analysis may also be applied to study the linear interference pattern of other localized waves. We believe that the results obtained by us shall be useful in soliton control, all-optical switching, and optical computing.