Solitonic wave structures to the (2 + 1)-dimensional cubic Klein–Gordon equation
Source abstract
Abstract
The objective of this paper is to investigate the solitonic waves structures to the (2 + 1)-dimensional cubic Klein–Gordon (2D-KG) equation. We employ the Riccati–Bernoulli (RB) sub-ODE approach to extract several types of solitary wave solutions for the 2D-KG model. The RB approach provides solutions in exponential, hyperbolic, trigonometric, and rational forms. This approach avoids laborious calculations and is simple, robust, and efficient. The solutions presented here are beneficial for elucidating various physical phenomena in nature, including plasma electromagnetic interactions, quantum mechanics, and relativistic hydrogen spectrum. Some 2D and 3D graphs are presented to demonstrate the shape of the obtained solutions for suitable values of the free parameters. We additionally demonstrate how the free parameters influence the behavior of the solutions. The results illustrate the simplicity and effectiveness of this method in generating complex nonlinear wave patterns and providing detailed, accurate solutions for nonlinear models in different fields of applied science.
Source: crossref · Quality: baseline
Research context
OpenAlex topics: Nonlinear Waves and Solitons · Nonlinear Photonic Systems · Advanced Mathematical Physics Problems
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
Affiliations
Department of Mathematics, College of Science, Taibah University , Al-Madinah Al-Munawarah,
References (25)
Show source-provided references
1. Nonlinearity contributions on critical MKP equation10.1080/16583655.2020.1774136 ↗
2. Similarity solutions of the newly derived magnetic model with damping effect and inhomogeneous exchange parameter in saturated ferromagnetic films10.1016/j.chaos.2024.115267 ↗
3. New study of (3 + 1)-dimensional nonlinear evolution equation with main part mKdV equation and novel solitary wave solutions10.1142/s021797922450293x ↗
4. New observation on the breather for a generalized nonlinear Schrödinger system with two higher-order dispersion operators in inhomogeneous optical fiber10.1016/j.ijleo.2018.12.148 ↗
5. A (2 + 1)-dimensional generalized Hirota–Satsuma–Ito equations: Lie symmetry analysis, invariant solutions and dynamics of soliton solutions10.1016/j.rinp.2021.104621 ↗
6. Binary Darboux transformation of vector nonlocal reverse-time integrable NLS equations10.1016/j.chaos.2024.114539 ↗
7. Investigation of exact solutions of nonlinear evolution equations using unified method10.3390/math10162996 ↗
8. Aggregation vs. global diffusive behavior in the higher-dimensional Keller–Segel model10.1016/j.jde.2010.02.008 ↗
9. Uniform-in-time boundedness in a class of local and nonlocal nonlinear attraction–repulsion chemotaxis models with logistics10.1016/j.nonrwa.2024.104135 ↗
10. Dissipative gradient nonlinearities prevent δ-formations in local and nonlocal attraction–repulsion chemotaxis models10.1111/sapm.70018 ↗
11. Multi-dark soliton solutions for the (2 + 1)-dimensional multi-component Maccari system10.1142/s0217984919503901 ↗
12. Some methods about finding the exact solutions of nonlinear modified BBM equation10.1155/2021/5564162 ↗
13. Generalized exp-function method to find closed form solutions of nonlinear dispersive modified Benjamin–Bona–Mahony equation defined by seismic sea waves10.3390/math10071026 ↗
14. Homotopy perturbation method for special nonlinear partial differential equations10.1016/j.jksus.2010.06.014 ↗
15. The (G′G)-expansion method and travelling wave solutions of nonlinear evolutions equations in mathematical physics10.1016/j.physleta.2007.07.051 ↗
16. New applications of variational iteration method10.1016/j.physd.2005.08.002 ↗
17. A Riccati-Bernoulli sub-ODE method for nonlinear partial differential equations and its application10.1186/s13662-015-0452-4 ↗
18. Exact solutions for nonlinear partial differential equations via Exp-function method10.1002/num.20497 ↗
19. 1-Soliton solution of KdV6 equation10.1007/s11071-014-1876-1 ↗
20. 1991
21. Generalized symmetries and conservation laws of (1 + 1)-dimensional Klein–Gordon equation10.1063/5.0003304 ↗
22. Exact solution of the one-dimensional Klein–Gordon equation with scalar and vector linear potentials in the presence of a minimal length10.1088/1674-1056/19/2/020305 ↗
23. Many new kinds exact solutions to (2 + 1)-dimensional Burgers equation and Klein–Gordon equation used a new method with symbolic computation10.1016/j.amc.2006.08.015 ↗
24. Nonlinear complex wave excitations in (2 + 1)-dimensional Klein–Gordon equation investigated by new wave transformation10.3390/math12182867 ↗
25. Numerical computation of Klein–Gordon equations arising in quantum field theory by using homotopy analysis transform method10.1016/j.aej.2014.02.001 ↗