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.

在本文中，研究了在具有非线性色散的二维电线中缝隙孤波的行为。应用半离散近似，我们表明网络中调制波的动力学可以用扩展的非线性Schrödinger方程来描述。借助动力学系统方法，我们检查了模型方程的不动点，并给出了其相图的分歧。同样，我们推导了亮孤子，暗孤子，峰值和反峰孤子，扭结和反扭孤子，周期解和一些在不同参数条件下对应于各个相像轨迹的紧凑子解的精确参数表示。