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Quasi-continuum approximations to lattice equations arising from the discrete nonlinear telegraph equation. (English) Zbl 0953.37022

The author analyses a transmission line composed of inductors and capacitors. The governing equations are discrete nonlinear equations. He investigates the types of solutions supportable by the system in seeking symmetry reductions. Approximate equations are obtained by replacing it with a local derivative operator. The quasi-continuum approximation technique makes use of higher-order derivatives to form more accurate approximations of the discrete difference operator via Padé approximants.

MSC:

37K60 Lattice dynamics; integrable lattice equations
34K07 Theoretical approximation of solutions to functional-differential equations
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