Construction of analytical solution for Hirota–Satsuma coupled KdV equation according to time via new approach: Residual power series
Source abstract
Abstract
In this work, a modern and novel approach method called the residual power series technique has been applied to find an analytical solution for an important equation in optical fibers called the Hirota–Satsuma coupled KdV equation with time as a series solution. Comparison of the analytical approximate solution with the exact solution concluded that the present method is an important addition for analyzing a system of partial differential equations that have a strong nonlinear term. We also represented graphically and discussed the effect of initial condition parameters and reaction of time on the model.
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Research context
OpenAlex topics: Fractional Differential Equations Solutions · Nonlinear Waves and Solitons · Nonlinear Photonic Systems
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Affiliations
Mathematics Department, Faculty of Education, University of Zakho 1 , Zakho, Kurdistan Region, Iraq
Mathematics Department, College of Science, University of Duhok 2 , Duhok, Kurdistan Region, Iraq
References (26)
Show source-provided references
1. Application of homotopy perturbation method to nonlinear wave equations10.1016/j.chaos.2005.03.006 ↗
2. Numerical simulation for fractional nonlinear (1 + 1)-dimensional Biswas–Milovic equation10.1016/j.ijleo.2017.02.016 ↗
3. Variational iteration method for delay differential equations10.1016/s1007-5704(97)90008-3 ↗
4. Approximate solutions for solving the Klein–Gordon and sine-Gordon equations10.1016/j.jaubas.2015.10.003 ↗
5. Numerical simulation of generalized Hirota–Satsuma coupled KdV equation by RDTM and comparison with DTM10.1016/j.cnsns.2011.05.022 ↗
6. The application of homotopy analysis method to solve a generalized Hirota–Satsuma coupled KdV equation10.1016/j.physleta.2006.09.105 ↗
7. Discrete homotopy analysis for optimal trading execution with nonlinear transient market impact10.1016/j.cnsns.2016.03.012 ↗
8. Thermal boundary layer analysis of nanofluid flow past over a stretching flat plate in different transpiration conditions by using DTM-Padé method10.22436/jmcs.017.01.08 ↗
9. A HAM-based wavelet approach for nonlinear ordinary differential equations10.1016/j.cnsns.2017.01.005 ↗
10. Soliton solutions of a coupled Korteweg-de Vries equation10.1016/0375-9601(81)90423-0 ↗
11. Variational iteration method for Hirota–Satsuma coupled KdV equation using auxiliary parameter10.1108/09615531211208006 ↗
12. Analytical approach to a generalized Hirota–Satsuma coupled Korteweg-de Vries equation by modified variational iteration method10.2298/TSCI1603885L ↗
13. The generalized nonlinear higher order of KdV equations from the higher order nonlinear Schrödinger equation and its solutions10.1016/j.ijleo.2017.03.086 ↗
14. Construction of exact solutions to the space–time fractional differential equations via new approach10.1016/j.ijleo.2016.11.139 ↗
15. Series solution of fuzzy differential equations under strongly generalized differentiability10.5373/jaram.1447.051912 ↗
16. Analytical solutions of fractional foam drainage equation by residual power series method10.1007/s40096-015-0141-1 ↗
17. A residual power series technique for solving Boussinesq–Burgers equations10.1080/23311835.2017.1279398 ↗
18. Residual power series method for solving time-space-fractional Benney-Lin equation arising in falling film problems10.1007/s12190-016-1056-1 ↗
19. Approximate analytical solutions of time fractional Whitham–Broer–Kaup equations by a residual power series method10.3390/e17096519 ↗
20. A representation of the exact solution of generalized Lane–Emden equations using a new analytical method10.1155/2013/378593 ↗
21. A reliable analytical method for solving higher-order initial value problems10.1155/2013/673829 ↗
22. New results on fractional power series: Theories and applications10.3390/e15125305 ↗
23. Approximate analytical solution of the nonlinear fractional KdV–Burgers equation: A new iterative algorithm10.1016/j.jcp.2014.08.004 ↗
24. Application of residual power series method for the solution of time-fractional Schrödinger equations in one-dimensional space10.3233/fi-2019-1795 ↗
25. Approximate solutions of nonlinear fractional Kundu-Eckhaus and coupled fractional massive Thirring equations emerging in quantum field theory using conformable residual power series method10.1088/1402-4896/abb420 ↗
26. An attractive analytical technique for coupled system of fractional partial differential equations in shallow water waves with conformable derivative10.1088/1572-9494/ab8a29 ↗