New insights into fractional twin-core couplers: bifurcation and sensitivity analysis
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...
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| Main Authors: | , , , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2024-11-01
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| Series: | Boundary Value Problems |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s13661-024-01941-4 |
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| Summary: | 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. |
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| ISSN: | 1687-2770 |