Periodic and Axial Perturbations of Chaotic Solitons in the Realm of Complex Structured Quintic Swift-Hohenberg Equation
Abstract
:1. Introduction
2. The Description of RMESEM
- Next, we hypothesise the following series-based solution for the NODE in (6) using the solution of the extended Riccati ODE:In this instance, represents the solution to the resulting extended Riccati ODE, and the variables and represent the unknown constants that must be calculated afterwards.
- Next, when (7) is incorporated in (6) or the equation resulting from the integration of (6), all the terms of are combined into an equal ordering. An expression in terms of is produced when this procedure is used. We obtain an algebraic system of equations describing the variables and with additional associated parameters by setting the coefficients in this equation to zero.
- An analytical evaluation of a collection of nonlinear algebraic equations is performed through the use of MAPLE.
- Then, by computing and inserting the unknown values in Equation (7) along together with (the Equation (8) answers), analytical soliton solutions for (5) are obtained. By employing (8)’s generic solution, we can derive multiple families of soliton solutions, which are shown in Table 1:where , , and .
3. Establishing Perturbed Soliton Solutions for CQSHE
4. Graphical Discussion
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
Appendix A
Appendix A.1. Comparison with Other Analytical Methods
References
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Iqbal, N.; Mohammed, W.W.; Alqudah, M.; Hamza, A.E.; Hussain, S. Periodic and Axial Perturbations of Chaotic Solitons in the Realm of Complex Structured Quintic Swift-Hohenberg Equation. Math. Comput. Appl. 2024, 29, 86. https://doi.org/10.3390/mca29050086
Iqbal N, Mohammed WW, Alqudah M, Hamza AE, Hussain S. Periodic and Axial Perturbations of Chaotic Solitons in the Realm of Complex Structured Quintic Swift-Hohenberg Equation. Mathematical and Computational Applications. 2024; 29(5):86. https://doi.org/10.3390/mca29050086
Chicago/Turabian StyleIqbal, Naveed, Wael W. Mohammed, Mohammad Alqudah, Amjad E. Hamza, and Shah Hussain. 2024. "Periodic and Axial Perturbations of Chaotic Solitons in the Realm of Complex Structured Quintic Swift-Hohenberg Equation" Mathematical and Computational Applications 29, no. 5: 86. https://doi.org/10.3390/mca29050086