THERMAL SCIENCE
International Scientific Journal
SOLITARY WAVE AND SINGULAR WAVE SOLUTIONS TO THE NEW (2+1)-D SHALLOW WATER WAVE EQUATION
ABSTRACT
The new (2+1)-D shallow water wave equation is considered in this research. Two effective methods, namely the Kudryashov method and the Bernoulli sub-equation function method are used to construct the diverse exact wave solutions. The solitary wave and singular wave solutions are obtained, The dynamic behaviors of the extracted wave solutions are unveiled graphically via MAPLE.
KEYWORDS
PAPER SUBMITTED: 2024-08-10
PAPER REVISED: 2024-09-17
PAPER ACCEPTED: 2024-12-07
PUBLISHED ONLINE: 2025-06-01
THERMAL SCIENCE YEAR
2025, VOLUME
29, ISSUE
Issue 2, PAGES [1569 - 1574]
- Hosseini, K., et al., The (2+1)-Dimensional Heisenberg Ferromagnetic Spin Chain Equation: Its Solitons and Jacobi Elliptic Function Solutions, The European Physical Journal Plus, 136 (2021), 2, pp. 1-9
- Hosseini, K., et al., New Exact Solutions of the Coupled Sine-Gordon Equations in Non-Linear Optics Using the Modified Kudryashov Method, Journal of Modern Optics, 65 (2018), 3, pp. 361-364
- Wang, K. L., New Perspective to the Coupled Fractional Non-linear Schrodinger Equations in Dual-Core Optical Fibers, Fractals, 33 (2025), ID2550034
- Duran, S., Dynamic Interaction of Behaviors of Time-fractional Shallow Water Wave Equation System, Modern Physics Letters B, 35 (2021), 22, ID2150353
- Liu, J. H., et al., On the Variational Principles of the Burgers-Korteweg-de Vries Equation in Fluid Mechanics, EPL, 149 (2025) 5, ID52001
- Raghda, A. M., et al., Optical Wave Solutions of the Higher-order Non-linear Schrödinger Equation with the Non-Kerr Non-Linear Term Via Modified Khater Method, Modern Physics Letters B, 34 (2020), 5, ID2050044
- Li, Y., et al., An Extended Hirota Bilinear Method and New Wave Structures of (2+1)-Dimensional Sawada-Kotera Equation, Applied Mathematics Letters, 145 (2023), ID108760
- Wang, K. J., et al., Novel Singular and Non-singular Complexiton, Interaction Wave and the Complex Multi-Soliton Solutions to the Generalized Non-Linear Evolution Equation, Modern Physics Letters B, 39 (2025), ID2550135
- Afzal, U., et al., On Soliton Solutions of Time Fractional Form of Sawada-Kotera Equation, Non-Linear Dynamics, 95 (2019), 1, pp. 391-405
- Raza, N., et al., Optical Dark and Dark-singular Soliton Solutions of (1+2)-Dimensional Chiral Non-Linear Schrodinger's Equation, Waves in Random and Complex Media, 29 (2019), 3, pp. 496-508
- Shang, D., Exact Solutions of Coupled Non-linear Klein-Gordon Equation, Applied Mathematics and Computation, 217 (2010), 4, pp. 1577-1583
- Zayed, E. M. E., et al., Optical Solitons in Birefringent Fibers with Kaup-Newell Equation Using Two Integration Schemes, Optik, 251 (2022), ID167992
- Wang, K. J., et al., Phase Portrait, Bifurcation and Chaotic Analysis, Variational Principle, Hamiltonian, Novel Solitary and Periodic Wave Solutions of the New Extended Korteweg-de Vries-Type Equation, Mathematical Methods in the Applied Sciences, On-line first, doi.org/10.1002/mma.10852, 2025
- Liang, Y. H., et al., Diverse Wave Solutions to the New Extended (2+1)-Dimensional Non-Linear Evolution Equation: Phase Portrait, Bifurcation and Sensitivity Analysis, Chaotic Pattern, Variational Principle and Hamiltonian, International Journal of Geometric Methods in Modern Physics, 22 (2025), ID2550158
- Han, P. F., et al., Backlund Transformation and Some Different Types of N‐soliton Solutions to the (3+1)‐Dimensional Generalized Non-Linear Evolution Equation for the Shallow‐water Waves, Mathematical Methods in the Applied Sciences, 44 (2021), 14, pp. 11307-11323
- Du, Z., et al., Backlund Transformation and Soliton Solutions in Terms of the Wronskian for the Kadomtsev-Petviashvili-Based System in Fluid Dynamics, Pramana, 90 (2018), 4, pp. 1-6
- Wang, K. L., New Dynamical Behaviors and Soliton Solutions of the Coupled Non-Linear Schrodinger Equation, International Journal of Geometric Methods in Modern Physics, 22 (2025), ID2550047
- Wang, K. L., et al., Novel Optical Soliton Solutions of the Fractional Perturbed Schrodinger Equation in Optical Fiber, Fractals, 33 (2025), ID2450147
- Rabie, W. B., et al., Cubic-Quartic Optical Solitons and other Solutions for Twin-core Couplers with Polynomial Law of Non-Linearity Using the Extended F-Expansion Method, Optik, 253 (2022), ID168575
- Abdullah, F. A., et al., Impressive and Innovative Soliton Shapes for Non-linear Konno-Oono Ssystem Relating to Electromagnetic Field, Optical and Quantum Electronics, 55 (2023), 1, ID69
- Wang, K. J, et al., Bifurcation Analysis, Chaotic Behaviors, Variational Principle, Hamiltonian and Diverse Optical Solitons of the Fractional Complex Ginzburg-Landau Model, International Journal of Theoretical Physics, On-line first: doi.org/10.1007/s10773-025-05977-9, 2025
- Wazwaz, A. M., New Integrable (2+1)-and (3+1)-Dimensional Shallow Water Wave Equations: Multiple Soliton Solutions and Lump Solutions, International Journal of Numerical Methods for Heat & Fluid-Flow, 32 (2022), 1, pp. 138-149
- Ryabov, P. N., et al., Application of the Kudryashov Method for Finding Exact Solutions of the High Order Non-Linear Evolution Equations, Applied Mathematics and Computation, 218 (2011), 7, pp. 3965-3972
- Akbar, M. A., et al., Soliton Solutions to the Boussinesq Equation through Sine-Gordon Method and Kudryashov Method, Results in Physics, 25 (2021), ID104228
- Wang, K. J., et al., Lump Wave, Breather Wave and the Other Abundant Wave Solutions to the (2+1)-Dimensional Sawada-Kotera-Kadomtsev Petviashvili Equation for Fluid Mechanic, Pramana, 99 (2025), 1, ID40