| Citation: |
Nauman Raza, Syeda Sarwat Kazmi, Ghada Ali Basendwah. DYNAMICAL ANALYSIS OF SOLITONIC, QUASI-PERIODIC, BIFURCATION AND CHAOTIC PATTERNS OF LANDAU-GINZBURG-HIGGS MODEL[J]. Journal of Applied Analysis & Computation, 2024, 14(1): 197-213. doi: 10.11948/20230137
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DYNAMICAL ANALYSIS OF SOLITONIC, QUASI-PERIODIC, BIFURCATION AND CHAOTIC PATTERNS OF LANDAU-GINZBURG-HIGGS MODEL
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Abstract
In this manuscript, the Landau-Ginzburg-Higgs (LGH) equation is considered as an investigating model. To extract novel results from the governing equation, the $ G'/(b G'+G+a) $-expansion approach has been employed. Utilizing this approach, the outcomes are attained as hyperbolic and trigonometric functions. Kink, periodic and singular soliton solutions have been recovered by selecting the appropriate values for the parameters. The obtained findings for the LGH equation are displayed in 3-D, contour and 2-D profiles. Using Galilean transformation, the model is converted into a planar dynamical system, and qualitative analysis is investigated. Moreover, chaotic and quasi-periodic patterns have been addressed after including the perturbed term. Simulated results reveal that by modifying amplitude and frequency parameters, the dynamic behavior of the system can also be changed. The recorded results are novel and show the effectiveness and feasibility of the suggested technique for assessing soliton solutions and phase visualizations for different nonlinear models.
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References
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Nauman Raza, Syeda Sarwat Kazmi, Ghada Ali Basendwah. DYNAMICAL ANALYSIS OF SOLITONIC, QUASI-PERIODIC, BIFURCATION AND CHAOTIC PATTERNS OF LANDAU-GINZBURG-HIGGS MODEL[J]. Journal of Applied Analysis & Computation, 2024, 14(1): 197-213. doi: 10.11948/20230137
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Figure 1.
3D, Contour and 2D plot for
$ V_{1,1}(x,t) $ $ \varrho= 2 $ $ \lambda =2 $ $ \vartheta = 0.5 $ $ b = 1 $ $ d=2.1 $ $ e=1 $ $ \mu=1 $ -
Figure 2.
3D, Contour and 2D plot for
$ V_{1,2}(x,t) $ $ \varrho= 2 $ $ \lambda =2 $ $ \vartheta = 0.5 $ $ b = 1 $ $ d=2.1 $ $ e=1 $ $ \mu=1 $ -
Figure 3.
3D, Contour and 2D plot for
$ V_{2,1}(x,t) $ $ \varrho= 1 $ $ \lambda =1 $ $ \vartheta = 1 $ $ b = 2 $ $ d=1 $ $ e=1 $ $ \mu=0.6 $ -
Figure 4.
3D, Contour and 2D plot for
$ V_{2,2}(x,t) $ $ \varrho= 1 $ $ \lambda =1 $ $ \vartheta = 1 $ $ b = 2 $ $ d=1 $ $ e=1 $ $ \mu=0.6 $ -
Figure 5.
Phase portrait for system (6.1), when
$ \zeta_1>0 $ $ \zeta_2>0 $ -
Figure 6.
Phase portrait for system (6.1), when
$ \zeta_1<0 $ $ \zeta_2<0 $ -
Figure 7.
For
$ \zeta_1=-3.2 $ $ \zeta_2 = 1.1 $ $ \delta_0 = 0.5 $ $ \omega =\pi $ -
Figure 8.
For
$ \zeta_1=-3.2 $ $ \zeta_2 = 1.1 $ $ \delta_0 = 1.5 $ $ \omega =\pi $ -
Figure 9.
For
$ \zeta_1=-3.2 $ $ \zeta_2 = 1.1 $ $ \delta_0 = 4.5 $ $ \omega =2\pi $ -
Figure 10.
For
$ \zeta_1=-3.2 $ $ \zeta_2 = 1.1 $ $ \delta_0 = 5.5 $ $ \omega =3\pi $