Investigating soliton dynamics: Contemporary computational and numerical approaches for analytical and approximate solutions of the CDG model
Source abstract
Abstract
This investigation employs contemporary computational and numerical techniques to derive analytical and approximate soliton solutions for the Caudrey–Dodd–Gibbon model, which represents a significant variation of the fifth-order Korteweg–de Vries equation. Diverse analytical solutions are constructed, employing distinct formats such as exponential, trigonometric, and hyperbolic functions. Simulations, including two-dimensional, three-dimensional, contour, polar, and discrete plots, are presented to illustrate the real-world behavior of a single soliton. Furthermore, these solutions are utilized to evaluate the essential conditions for implementing the proposed numerical scheme. The agreement between the computed and approximate solutions is demonstrated through various techniques. These results unequivocally establish the superiority of these methods for solving nonlinear mathematical physics problems.
Source: crossref · Quality: baseline
Research context
OpenAlex topics: Nonlinear Waves and Solitons · Fractional Differential Equations Solutions · Numerical methods for differential equations
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
Affiliations
School of Medical Informatics and Engineering, Xuzhou Medical University 1 , 209 Tongshan Road, 221004 Xuzhou, Jiangsu Province, People’s Republic of China
Department of Basic Science, Obour High Institute for Engineering and Technology 2 , 11828 Cairo, Egypt
Key Laboratory of Acupuncture and Medicine Research of Ministry of Education, Nanjing University of Chinese Medicine 3 , Nanjing 210023, People’s Republic of China
Department of Basic Science, Higher Technological Institute 10th of Ramadan City 4 , El Sharqia 44634, Egypt
Funding
Unveiling and Leading Project of XZHMU
References (34)
Show source-provided references
1. Plenty of accurate novel solitary wave solutions of the fractional Chaffee–Infante equation10.1016/j.rinp.2023.106400 ↗
2. Novel soliton wave solutions of a special model of the nonlinear Schrödinger equations with mixed derivatives10.1016/j.rinp.2023.106367 ↗
3. Novel computational simulation of the propagation of pulses in optical fibers regarding the dispersion effect10.1142/s0217979223500832 ↗
4. A hybrid analytical and numerical analysis of ultra-short pulse phase shifts10.1016/j.chaos.2023.113232 ↗
5. Modeling of plasma wave propagation and crystal lattice theory based on computational simulations10.1063/5.0146462 ↗
6. Analytically and numerically, dispersive, weakly nonlinear wave packets are presented in a quasi-monochromatic medium10.1016/j.rinp.2023.106312 ↗
7. Effect of adding nano-materials on the properties of hydroxypropyl methylcellulose (HPMC) edible films10.1038/s41598-023-32218-y ↗
8. Prorogation of waves in shallow water through unidirectional Dullin–Gottwald–Holm model; computational simulations10.1142/s0217979223500716 ↗
9. Solid physics equations, accurate and novel soliton wave structures for heating a single crystal of sodium fluoride10.1142/s0217979223500686 ↗
10. Nonlinear elastic circular rod with lateral inertia and finite radius: Dynamical attributive of longitudinal oscillation10.1142/s0217979223500522 ↗
11. Computational and numerical simulations of the wave propagation in nonlinear media with dispersion processes10.1063/5.0143256 ↗
12. Accurate computational simulations of perturbed Chen–Lee–Liu equation10.1016/j.rinp.2023.106227 ↗
13. Effects of integrability criterion on nonlinear Schrödinger equations with mixed derivatives: Insights from the Rangwala–Rao equation10.1007/s11082-023-04993-5 ↗
14. Multi-vector with nonlocal and non-singular kernel ultrashort optical solitons pulses waves in birefringent fibers10.1016/j.chaos.2022.113098 ↗
15. Abundant solitary and semi-analytical wave solutions of nonlinear shallow water wave regime model
16. Physics of crystal lattices and plasma; analytical and numerical simulations of the Gilson–Pickering equation10.1016/j.rinp.2022.106193 ↗
17. Nonlinear biological population model; computational and numerical investigations10.1016/j.chaos.2022.112388 ↗
18. Computational investigation on a nonlinear dispersion model with the weak non-local nonlinearity in quantum mechanics10.1016/j.rinp.2022.105583 ↗
19. Ultra-short pulses generation’s precise influence on the light transmission in optical fibers10.1016/j.rinp.2022.105411 ↗
20. Nonparaxial pulse propagation in a planar waveguide with Kerr-like and quintic nonlinearities; computational simulations10.1016/j.chaos.2022.111970 ↗
21. Lax representation and bi-Hamiltonian structure of nonlinear Qiao model10.1142/s0217984921506144 ↗
22. Diverse soliton wave solutions of for the nonlinear potential Kadomtsev–Petviashvili and Calogero–Degasperis equations10.1016/j.rinp.2021.105116 ↗
23. Abundant accurate analytical and semi-analytical solutions of the positive Gardner–Kadomtsev–Petviashvili equation10.1515/phys-2022-0001 ↗
24. Numerical simulation of fifth order KdV equations occurring in magneto-acoustic waves10.1016/j.asej.2017.03.004 ↗
25. Travelling wave solutions of the generalized nonlinear fifth-order KdV water wave equations and its stability10.1016/j.jtusci.2016.06.002 ↗
26. Two-mode fifth-order KdV equations: Necessary conditions for multiple-soliton solutions to exist10.1007/s11071-016-3144-z ↗
27. A fifth-order Korteweg–de Vries equation for shallow water with surface tension: Multiple soliton solutions10.12693/aphyspola.130.679 ↗
28. Computational and numerical wave solutions of the Caudrey–Dodd–Gibbon equation10.1016/j.heliyon.2023.e13511 ↗
29. Generalized fifth-order nonlinear evolution equation for the Sawada–Kotera, Lax, and Caudrey–Dodd–Gibbon equations in plasma physics: Painlevé analysis and multi-soliton solutions10.1088/1402-4896/ac4f9d ↗
30. Laplace transform: Making the variational iteration method easier10.1016/j.aml.2019.01.016 ↗
31. A general numerical algorithm for nonlinear differential equations by the variational iteration method10.1108/HFF-01-2020-0029 ↗
32. Variational iteration algorithm-I with an auxiliary parameter for wave-like vibration equations10.1177/1461348418823126 ↗
33. Stability of a class of delayed port-Hamiltonian systems with application to microgrids with distributed rotational and electronic generation10.1016/j.automatica.2016.07.022 ↗
34. On the passivity based control of irreversible processes: A port-Hamiltonian approach10.1016/j.automatica.2015.07.002 ↗