Dressed shock waves in a nonlinear LC circuit

Nonlinear shock waves which appear in a nonlinear Toda lattice with internal dissipation have been studied. The tanh method is used as a perturbation approach together with the assumption of long wavelengths. Moreover, asymptotical behaviour is used to determine the velocity. Burgers-like wave solutions up to third order are derived. If the amplitude of the shock wave is given, the profiles are readjusted to match this boundary condition. The associated steepness and velocity of the solution can be written as a function of this boundary condition.