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More on Transmission-Line Solitons

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The study of solitons on discrete lattices dates back to the early days of soliton theory (Frenkel and Kontorova 1939, Fermi et al. 1955) and is of great physical importance. Generally, the discrete nonlinear equations which model these lattices cannot be solved analytically. Consequently, one looks for possible pulse-soliton solutions in the continuum or long wavelength approximation, that is, solitons with a width much larger than the electrical length of a unit section of the electrical network, as described in Chap.3. When this approach is not workable, one has to use numerical approaches (Zabusky 1973, Eilbeck 1991) or simulations. Nevertheless, there exist some lattice models for which the governing equations can be solved exactly. This is the case for the lattice with exponential interactions, introduced in 1967 by Toda (see also Chap.9).