New insights into fractional twin-core couplers: bifurcation and sensitivity analysis

Abstract

Abstract This paper analyses the analytical solutions of the fractional twin-core coupler (fTCC) equations, which include Kerr law nonlinearity, utilising the unified and sub-ODE methods along with beta and M-truncated fractional derivatives. The visually detailed report highlights certain solutions adorned with carefully selected parametric values to demonstrate their distribution. The main concept of this enhancement involves adopting a new formal structure for the preferred solution and considering the dynamic aspects of the problem. To achieve a more profound comprehension of physical implications of these solutions, we have depicted them through diverse visualisations, including 3D and 2D plots. Subsequently, a planar dynamical system is introduced, and bifurcation analysis is performed to determine the bifurcation structures of the nonlinear and super-nonlinear travelling wave solutions of the proposed model. Every potential phase portrait is displayed using specific parameter values. Finally, the model is transformed via the Galilean transformation into a planer dynamical system and the sensitivity performance is assessed.

Keywords

• Beta-derivative
• M-truncated derivative
• Analytical solutions
• Unified method
• Sub-ODE method
• Phase portraits