| Citation: |
A. Tripathy, S. Sahoo, S. Saha Ray, M. A. Abdou. COMPLEX NONLINEAR EVOLUTION EQUATIONS IN THE CONTEXT OF OPTICAL FIBERS: NEW WAVE-FORM ANALYSIS[J]. Journal of Applied Analysis & Computation, 2023, 13(6): 3442-3460. doi: 10.11948/20230080
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COMPLEX NONLINEAR EVOLUTION EQUATIONS IN THE CONTEXT OF OPTICAL FIBERS: NEW WAVE-FORM ANALYSIS
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Abstract
In this study, the new waveforms of two nonlinear evolution models are investigated by an analytical method, namely the sigmoid function method. The considered nonlinear complex models for this are the full nonlinearity form of the Fokas-Lenells equation and the paraxial wave equation, which play an important role in the field of fiber optics by balancing the nonlinearity with the dispersion terms. Under different numeric values of the free terms, the obtained results represent varieties of wave shapes, specifically anti-kink, dark, bright, singular soliton, anti-peakon, kink, two-lump propagation during breather periodic form, single lump, two lump solutions, periodic peakon, and periodic wave solutions, which have not been obtained in the previous studies. These dynamical characteristics are discussed in detail with the help of a pictorial presentation of the derived solutions. These resultants of both the considered nonlinear equations can be useful in both fiber optics as well as in other optics-related fields.
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References
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A. Tripathy, S. Sahoo, S. Saha Ray, M. A. Abdou. COMPLEX NONLINEAR EVOLUTION EQUATIONS IN THE CONTEXT OF OPTICAL FIBERS: NEW WAVE-FORM ANALYSIS[J]. Journal of Applied Analysis & Computation, 2023, 13(6): 3442-3460. doi: 10.11948/20230080
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Figure 1.
Wave solutions of eq.(3.5) for
$ a_{1}=-1.2, a_{2}=0.3, \alpha=2, l=0.2, \delta=-1.5 $ $ q=-0.01 $ -
Figure 2.
Wave solutions of eq.(3.7) for
$ a_{1}=1.2, a_{2}=0.3, \alpha=2, l=0.2, \delta=0.5 $ $ q=-1 $ -
Figure 3.
Wave solutions of eq.(3.9) for
$ a_{1}=-1.2, a_{2}=0.3, \alpha=2, l=0.2, \delta=0.5 $ $ q=-1 $ -
Figure 4.
Wave solutions of eq.(3.10) for
$ a_{1}=-0.2, a_{2}=-0.3, m=2, \alpha=-2, l=-0.2, \delta=0.05 $ $ q=0.01 $ -
Figure 5.
Wave solutions of eq.(3.12) for the values of
$ a_{1}=1.2, m=-0.3, a_{3}=-2, l=-0.2, q=-0.1 $ $ y=-0.5 $ -
Figure 6.
Wave solutions of eq.(3.12) for the values of
$ a_{1}=-1.2, m=-0.3, a_{3}=-1.38, l=0.2, q=0.65 $ $ y=-0.5 $ -
Figure 7.
Wave solutions of eq.(3.13) for the values of
$ a_{1}=-1.2, m=-0.3, a_{3}=1.38, l=0.2 $ $ y=0.5 $ -
Figure 8.
Wave solutions of eq.(3.13) for the values of
$ a_{1}=-1.9, m=-0.3, a_{3}=-1.38, l=-2.2 $ $ y=-1.5 $ -
Figure 9.
Wave solutions of eq.(3.13) for the values of
$ a_{1}=-1.9, m=-0.3, a_{3}=-0.38, l=0.2 $ $ y=-0.5 $ -
Figure 10.
Wave solutions of eq.(3.14) for the values of
$ a_{1}=1.9, m=-0.3, a_{3}=1.38, l=-2.2 $ $ y=-1.5 $ -
Figure 11.
Wave solutions of eq.(3.14) for the values of
$ a_{1}=-1.9, m=-0.3, a_{3}=-0.38, l=-1.82 $ $ y=-1.5 $ -
Figure 12.
Wave solutions of eq.(3.15) for the values of
$ a_{1}=-1.9, m=-0.3, a_{3}=-1.38, l=-2.2 $ $ y=-0.5 $ -
Figure 13.
Wave solutions of eq.(3.15) for the values of
$ a_{1}=-1.9, m=-0.3, a_{3}=1.38, l=-2.2 $ $ y=1.5 $