TWO-DIMENSIONAL ARRAY CASUSED BY ABLOWITZ-LADIK-HIROTA WAVE GUIDE COMPLEXITY

We prove that the rational solutions exist for the integrable version of the discretized nonlinear Schrödinger equation known as the Ablowitz-Ladik equation, which exhibits rogue wave behavior. We establish the existence of a pecking order among rational solutions, and then use the Hirota method to deduce the first two solutions in that order. The stability of discrete similaritons and first-order rogue waves propagating across nonlinear waveguide arrays may be simulated by means of the inhomogeneous ALH equation. The similarity transformation is used to find these nonlinear solutions. Complexity and stability in discrete or continuous spatial configurations are the focus of CC, a CIM. When the amplitude modulation parameter is set to illustrative values, we discovered that the CC demonstrates saturation for a longer duration for rogue waves and a shorter time for free waves. We also provide rational solutions for the more general discrete Hirota equation, which includes the discrete Ablowitz-Ladik equation and the discrete modified Korteweg-de Vries mKdV equation as special instances.