Bifurcation of gap solitary waves in a two-dimensional electrical network with nonlinear dispersion

In this paper, the behavior of gap solitary waves is investigated in a two-dimensional electrical line with nonlinear dispersion. Applying the semidiscrete approximation, we show that the dynamics of modulated wave in the network can be described by an extended nonlinear Schrödinger equation. With the aid of the dynamical systems approach, we examine the fixed points of our model equation and the bifurcations of its phase portrait are presented. Likewise, we derive the exact parametric representations of bright soliton, dark soliton, peak and anti-peak solitons, kink and anti-kink solitons, periodic solutions and some compacton solutions corresponding to the various phase portrait trajectories under different parameter conditions. We find out that the nonlinear dispersion considerably affects the dynamics of the system and leads to a number of new solitary-wave solutions, namely, peakon, periodic peakon, compacton solutions, which can not be observed when the dispersion is assumed linear.