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Cusp solitons, shock waves and envelope solitons in a new non-linear transmission line

1987; Institute of Physics; Volume: 20; Issue: 7 Linguagem: Inglês

10.1088/0305-4470/20/7/019

1361-6447

Y. N. Nejoh,

Nonlinear Photonic Systems

A new non-linear evolution equation is derived in the continuum limit of a dispersive non-linear transmission line. Since this equation has a similar structure to the Boussinesq equation, but with the non-linear term of higher-order derivatives, it can be called the derivative Boussinesq equation. This equation bears a cusp soliton. A solution for the voltage signal exhibits a shock-wave front. The asymptotic behaviour of this equation is related to the non-linear Schrodinger equation by the reductive perturbation method. Its solitary wave solution is expressed in terms of the bright-envelope soliton. Hence, the non-linear transmission line proposed in the present paper describes the density depression, the collisionless shock wave in plasmas and the modulation instability of the asymptotic wave propagating in this line.