Analyzing sensitivity and multi-soliton solutions in the Estevez–Mansfield–Clarkson equation: Insights into dynamics of bifurcation and chaos

Abstract

In this investigation, an analysis of the Estevez–Mansfield–Clarkson equation, a model equation employed in the examination of shape formation in liquid drops, optics, and mathematical physics, is undertaken. Firstly, multiple wave solitons, including 1-soliton, 2-soliton, and 3-soliton structures, are successfully generated through the utilization of a multiple exp-function technique. Subsequently, the conversion of the partial differential equation into an ordinary differential equation is executed. The extraction of various traveling wave patterns, such as kink, anti-kink, periodic, and exponential functions, is then carried out using the new auxiliary equation method. The outcomes are visually represented through 3-dimensional, 2-dimensional, and density plots, employing Mathematica software. Following this, an investigation into the qualitative dynamics of the equation is conducted, examining aspects such as bifurcation and chaos. Critical points are identified for bifurcation, and the dynamical system undergoes an outward force, resulting in the identification of chaotic patterns. Furthermore, the model’s sensitivity across different initial values is explored. These solutions hold immense significance in the domains of nonlinear fiber optics and telecommunications that help in deepening our knowledge about the basic physical model.