Exact soliton solutions of coupled nonlinear Schrödinger equations: shape-changing collisions, logic gates, and partially coherent solitons.

Abstract

The different dynamical features underlying soliton interactions in coupled nonlinear Schrödinger equations, which model multimode wave propagation under varied physical situations in nonlinear optics, are studied. In this paper, by explicitly constructing multisoliton solutions (up to four-soliton solutions) for two-coupled and arbitrary N-coupled nonlinear Schrödinger equations using the Hirota bilinearization method, we bring out clearly the various features underlying the fascinating shape changing (intensity redistribution) collisions of solitons, including changes in amplitudes, phases and relative separation distances, and the very many possibilities of energy redistributions among the modes of solitons. However, in this multisoliton collision process the pairwise collision nature is shown to be preserved in spite of the changes in the amplitudes and phases of the solitons. Detailed asymptotic analysis also shows that when solitons undergo multiple collisions, there exists the exciting possibility of shape restoration of at least one soliton during interactions of more than two solitons represented by three- and higher-order soliton solutions. From an application point of view, we have shown from the asymptotic expressions how the amplitude (intensity) redistribution can be written as a generalized linear fractional transformation for the N-component case. Also we indicate how the multisolitons can be reinterpreted as various logic gates for suitable choices of the soliton parameters, leading to possible multistate logic. In addition, we point out that the various recently studied partially coherent solitons are just special cases of the bright soliton solutions exhibiting shape-changing collisions, thereby explaining their variable profile and shape variation in collision process.