Abstract
In this chapter we sketch the basic mathematical notions of dynamical projection used in this book, starting from general relations and illustrating them by the simplest examples, following [1,2,3] and paying particular attention to the impact of inhomogeneities and accompanying effects. As mentioned in the introduction [see (1.1)], in the waveguide propagation, after expanding all the fields in series over the transverse coordinate basis, the coefficients \(\psi _k\) of the expansions will depend on the unique longitudinal space coordinate, say x, and time. Let \(\partial ={\partial }/{\partial x}\) denote the space derivative.
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Leble, S. (2019). Evolution Operator and Projectors to Its Eigenspaces. In: Waveguide Propagation of Nonlinear Waves. Springer Series on Atomic, Optical, and Plasma Physics, vol 109. Springer, Cham. https://doi.org/10.1007/978-3-030-22652-7_2
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