Transverse compactlike pulse signals in a two-dimensional nonlinear electrical network

We investigate the compactlike pulse signal propagation in a two-dimensional nonlinear electrical transmission network with the intersite circuit elements (both in the propagation and transverse directions) acting as nonlinear resistances. Model equations for the circuit are derived and can reduce from the continuum limit approximation to a two-dimensional nonlinear Burgers equation governing the propagation of the small amplitude signals in the network. This equation has only the mass as conserved quantity and can admit as solutions cusp and compactlike pulse solitary waves, with width independent of the amplitude, according to the sign of the product of its nonlinearity coefficients. In particular, we show that only the compactlike pulse signal may propagate depending on the choice of the realistic physical parameters of the network, and next we study the dissipative effects on the pulse dynamics. The exactness of the analytical analysis is confirmed by numerical simulations which show a good agreement with results predicted by the Rosenau and Hyman K(2,2) equation.