Diverse novel analytical and semi-analytical wave solutions of the generalized (2+1)-dimensional shallow water waves model
Source abstract
Abstract
This article studies the generalized (2 + 1)-dimensional shallow water equation by applying two recent analytical schemes (the extended simplest equation method and the modified Kudryashov method) for constructing abundant novel solitary wave solutions. These solutions describe the bidirectional propagating water wave surface. Some obtained solutions are sketched in two- and three-dimensional and contour plots for demonstrating the dynamical behavior of these waves along shallow water. The accuracy of the obtained solutions and employed analytical schemes is investigated using the evaluated solutions to calculate the initial condition, and then the well-known variational iterational (VI) method is applied. The VI method is one of the most accurate semi-analytical solutions, and it can be applied for high derivative order. The used schemes’ performance shows their effectiveness and power and their ability to handle many nonlinear evolution equations.
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Research context
OpenAlex topics: Nonlinear Waves and Solitons · Ocean Waves and Remote Sensing · Differential Equations and Numerical Methods
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
Affiliations
Department of Mathematics, Huzhou University 1 , Huzhou 313000, China
Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering, Changsha University of Science and Technology 2 , Changsha 410114, China
Department of Mathematics, Faculty of Science, Jiangsu University 3 , 212013 Zhenjiang, China
Department of Mathematics, Obour Institutes 4 , 11828 Cairo, Egypt
Department of Mathematics and Statistics, College of Science, Taif University 5 , P. O. Box 11099, Taif 21944, Saudi Arabia
Department of Physics and Engineering Mathematics, Faculty of Electronic Engineering, Menoufia University 6 , Menoufia 32952, Egypt
Funding
Taif University · National Natural Science Foundation of China-Guangdong Joint Fund
References (34)
Show source-provided references
1. The dynamical behavior of mixed type lump solutions on the (3+1)-dimensional generalized Kadomtsev–Petviashvili–Boussinesq equation10.1515/ijnsns-2018-0373 ↗
2. Exact optical solitons of the perturbed nonlinear Schrödinger–Hirota equation with Kerr law nonlinearity in nonlinear fiber optics10.1515/phys-2020-0177 ↗
3. Investigation of solitons and mixed lump wave solutions with (3+1)-dimensional potential-YTSF equation10.1016/j.cnsns.2020.105544 ↗
4. Novel explicit solutions for the nonlinear Zoomeron equation by using newly extended direct algebraic technique10.1007/s11082-019-2162-8 ↗
5. Modulation instability analysis, optical and other solutions to the modified nonlinear Schrödinger equation10.1088/1572-9494/ab7ec8 ↗
6. Generalized logistic equation method for Kerr law and dual power law Schrödinger equations10.1007/s11082-020-02611-2 ↗
7. Rogue wave solutions and modulation instability with variable coefficient and harmonic potential10.3389/fphy ↗
8. Coherent large-scale structures from the linearized Navier–Stokes equations10.1017/jfm.2019.391 ↗
9. Chirped solitons in optical monomode fibres modelled with Chen–Lee–Liu equation10.1007/s12043-019-1872-6 ↗
10. A reliable algorithm for time-fractional Navier-Stokes equations via Laplace transform10.1515/nleng-2018-0080 ↗
11. Steady Navier–Stokes equations in planar domains with obstacle and explicit bounds for unique solvability10.1007/s00205-020-01565-9 ↗
12. Optical solitons in (n+ 1) dimensions with Kerr and power law nonlinearities10.1142/s021798491750186x ↗
13. Solitary wave solutions for the generalized Zakharov--Kuznetsov--Benjamin--Bona--Mahony nonlinear evolution equation10.1016/J.JOES.2017.05.002 ↗
14. Oblique explicit wave solutions of the fractional biological population (BP) and equal width (EW) models10.1186/s13662-020-03005-0 ↗
15. Abundant distinct types of solutions for the nervous biological fractional Fitzhugh–Nagumo equation via three different sorts of schemes10.1186/s13662-020-02852-1 ↗
16. On abundant new solutions of two fractional complex models10.1186/s13662-020-02705-x ↗
17. The plethora of explicit solutions of the fractional KS equation through liquid–gas bubbles mix under the thermodynamic conditions via Atangana–Baleanu derivative operator10.1186/s13662-020-2540-3 ↗
18. Dynamical behaviour of the light pulses through the optical fiber: Two nonlinear atangana conformable fractional evolution equations10.1155/2020/8862484 ↗
19. On highly dimensional elastic and nonelastic interaction between internal waves in straight and varying cross-section channels10.1155/2020/5010589 ↗
20. Two effective computational schemes for a prototype of an excitable system10.1063/5.0024417 ↗
21. Computational solutions of the HIV-1 infection of CD4+ T-cells fractional mathematical model that causes acquired immunodeficiency syndrome (AIDS) with the effect of antiviral drug therapy10.1016/j.chaos.2020.110092 ↗
22. On the analytical and numerical solutions in the quantum magnetoplasmas: The atangana conformable derivative (2+1)-ZK equation with power-law nonlinearity10.1155/2020/5809289 ↗
23. On the numerical investigation of the interaction in plasma between (high & low) frequency of (Langmuir & ion-acoustic) waves10.1016/j.rinp.2020.103317 ↗
24. Modified Laplace variational iteration method for solving fourth-order parabolic partial differential equation with variable coefficients10.1016/j.camwa.2019.03.053 ↗
25. Abundant analytical and numerical solutions of the fractional microbiological densities model in bacteria cell as a result of diffusion mechanisms10.1016/j.chaos.2020.109824 ↗
26. Inelastic interaction and blowup new solutions of nonlinear and dispersive long gravity waves10.1155/2020/5362989 ↗
27. M-lump, interaction between lumps and stripe solitons solutions to the (2+1)-dimensional KP-BBM equation10.1140/epjp/s13360-020-00109-0 ↗
28. Lie symmetries, optimal system and dynamics of exact solutions of (2+1)-dimensional KP-BBM equation10.1088/1402-4896/ab8651 ↗
29. Exact solutions and conservation laws of a (2+ 1)-dimensional nonlinear KP-BBM equation
30. Extended simplest equation method for nonlinear differential equations10.1016/j.amc.2008.08.019 ↗
31. An extended simplest equation method and its application to several forms of the fifth-order KdV equation10.1016/j.amc.2010.04.029 ↗
32. New exact solutions of nonlinear conformable time-fractional Boussinesq equations using the modified Kudryashov method10.1080/17455030.2017.1296983 ↗
33. Modified Kudryashov method via new exact solutions for some conformable fractional differential equations arising in mathematical biology10.1016/j.cjph.2017.11.020 ↗
34. Laplace transform: Making the variational iteration method easier10.1016/j.aml.2019.01.016 ↗