Abstract
A lot has been written [1] about temporal soliton coupling using various forms of coupled Schrödinger equations and widely differing methods of solutions. They range from being almost entirely mathematical, through mixed approaches, based upon linear stability analysis, to being entirely variational [2–5]. The problems already addressed in this group have used generic coupled Schrödinger equations to yield soliton dynamics, expressed in terms of linear coupling and nonlinear coupling parameters. In this context, polarisation-coupled spatial sohtons [6] in optical planar waveguides have been investigated using Whitham’s [7] average variational principle. It is encouraging that analytical forms of the so-called stability edges have been found and the numerical work provided confirms that the true solitons agree with the mathematical analysis. In addition, the behaviour of spatial solitions in coupled planar optical waveguides has been investigated in a theory that includes all the nonlinear cross-phase modulation terms [4]. Here, problems addressed concern spatial soliton beam displacement, beam switching, and a number of stability problems. It is safe to say, then, that significant mathematical progress has been made and that, in every case, it has been verified by accurate [exact] numerical simulation.
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Boardman, A.D., Xie, K. (1998). Spatial Solitons in x(2) and (3) Dielectrics and Control by Magnetooptic Materials. In: Moloney, J.V. (eds) Nonlinear Optical Materials. The IMA Volumes in Mathematics and its Applications, vol 101. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1714-5_4
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DOI: https://doi.org/10.1007/978-1-4612-1714-5_4
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