Construction of Exact Solutions for Gilson–Pickering Model Using Two Different Approaches
Abstract
:1. Introduction
2. Methodology of Extended Simple Equation Method
- Step 1:
- Let the PDE have the form
- Step 2:
- Consider the wave transformation:
- Step 3:
- Consider that Equation (7) has a solution of the form
- Step 4:
- Let satisfy the DE of the form
3. Methodology of Generalized Riccati Equation Mapping Method
- Step 3:
- Let the solution for Equation (7) have the form
- Type 1:
- When and or , the solutions of Equation (16) are given as
- Type 2:
- When and or , the solutions of Equation (16) are given as
- Type 3:
- When and , the solutions of Equation (16) are given as
- Type 4:
- When and , the only solution of Equation (16) is
4. Application of Extended Simple Equation Method
- Case 1:
- If
- Case 2:
- If , .
- Case 3:
- If , .
5. Application of Generalized Riccati Equation Mapping Method:
- Type 1:
- When and or , the solutions of Equation (18) are
- Type 2:
- When and or , the solutions of Equation (18) are
- Type 3:
- When and , the solutions of Equation (18) are
- Type 4:
- When and , the only solution of Equation (18) is
6. Results and Discussion
7. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Rehman, H.U.; Awan, A.U.; Tag-ElDin, E.M.; Bashir, U.; Allahyani, S.A. Construction of Exact Solutions for Gilson–Pickering Model Using Two Different Approaches. Universe 2022, 8, 592. https://doi.org/10.3390/universe8110592
Rehman HU, Awan AU, Tag-ElDin EM, Bashir U, Allahyani SA. Construction of Exact Solutions for Gilson–Pickering Model Using Two Different Approaches. Universe. 2022; 8(11):592. https://doi.org/10.3390/universe8110592
Chicago/Turabian StyleRehman, Hamood Ur, Aziz Ullah Awan, ElSayed M. Tag-ElDin, Uzma Bashir, and Seham Ayesh Allahyani. 2022. "Construction of Exact Solutions for Gilson–Pickering Model Using Two Different Approaches" Universe 8, no. 11: 592. https://doi.org/10.3390/universe8110592