Finding Powerful Solutions for the Generalized Hyperelastic-Rod Wave Equation

Abstract

In this paper, the generalized hyperelastic rod wave equation has been studied. The generalized exponential rational function method (GERFM) has been applied to the generalized hyperelastic rod wave equation. Thus, some new and abundant soliton solutions of the generalized hyperelastic rod wave equation have been obtained. Also, in Wolfram Mathematica 12, both 2D and 3D shapes of these built-in results have been plotted.

Keywords

• GERFM
• Generalized hyperelastic-rod wave equation
• soliton solutions.

References

1. [1] M.M.A. Khater and A.M. Alabdali, Multiple Novels and Accurate TravelingWave and NumericalSolutions of the (2+1) Dimensional Fisher-Kolmogorov- Petrovskii-Piskunov Equation, Mathematics, 9(12) (2021), 1-13.
2. [2] F. Dusunceli, E. Celik, M. Askin and H. Bulut, New exact solutions for the doubly dispersive equation using the improved Bernoulli sub-equation function method, Indian Journal of Physics, 95(2) (2021), 309-314.
3. [3] G. Bakıcıerler, S. Alfaqeih and E. Mısırlı, Analytic solutions of a (2+1)-dimensional nonlinear Heisenberg ferromagnetic spin chain equation, Physica A: Statistical Mechanics and its Applications, 582 (2021), 126255.
4. [4] S. Malik, S. Kumar, K.S. Nisar and C.A. Saleel, Different analytical approaches for finding novel optical solitons withgeneralized third-order nonlinear Schr¨odinger equation, Results in Physics, 29 (2021), 104755.
5. [5] T. Akt¨urk, Y. Gurefe and Y. Pandir, An application of the new function method to the Zhiber–Shabat equation, An International Journal of Optimization and Control: Theories Applications (IJOCTA), 7(3) (2017), 271–274.
6. [6] A. Akbulut, M. Kaplan and F. Tascan, The investigation of exact solutions of nonlinear partial differential equations by using exp (􀀀f(x )) method, Optik, 132 (2017), 382–387.
7. [7] M. U¨ nal and M. Ekici, The Double (G0=G;1=G)-Expansion Method and Its Applications for Some Nonlinear Partial Differential Equations, Journal of the Institute of Science and Technology, 11(1) (2021), 599-608.
8. [8] R.I. Nuruddeen, K. S. Aboodh and K. K. Ali, Analytical Investigation of Soliton Solutions to Three Quantum Zakharov-Kuznetsov Equations, Communications in Theoretical Physics, 70(4) (2018), 405-412.

9. [9] M. Tahir and A. U. Awan, Optical singular and dark solitons with Biswas–Arshed model by modified simple equation method, Optik, 202 (2020), 163523.
10. [10] O. Tasbozan, Y. C¸ enesiz and A. Kurt, New solutions for conformable fractional Boussinesq and combined KdV-mKdV equations using Jacobi elliptic function expansion method, The European Physical Journal Plus, 131 (2016), 244.
11. [11] H.F. Ismael, H. Bulut and H.M. Baskonus, W-shaped surfaces to the nematic liquid crystals with three nonlinearity laws, Soft Computing, 25 (2021), 4513–4524.
12. [12] H.F. Ismael, M.A.S Murad and H. Bulut, Various exact wave solutions for KdV equation with time-variable coefficients, Journal of Ocean Engineering and Science, 7(5) (2022), 409–418.
13. [13] H.F. Ismael and H. Bulut, On the Wave Solutions of (2+1)-Dimensional Time-Fractional Zoomeron Equation, Konuralp Journal of Mathematics, 8(2) (2020), 410–418.
14. [14] H.F. Ismael, S.S. Atas, H. Bulut and M.S. Osman, Analytical solutions to the M-derivative resonant Davey–Stewartson equations, Modern Physics Letters B, 35(30) (2021), 2150455.
15. [15] H.F. Ismael and H. Bulut, Nonlinear dynamics of (2+1)-dimensional Bogoyavlenskii–Schieff equation arising in plasma physics, Mathematical Methods in the Applied Sciences, 44(13) (2021), 10321–10330.
16. [16] S. Akcagil, T. Aydemir and O.F. Gozukizil, Exact travelling wave solutions of nonlinear pseudoparabolic equations by using the (G0=G) Expansion Method, New Trends in Mathematical Sciences, 4(4) (2016), 51-66.
17. [17] O.F. Gozukizil and S. Akcagil, The tanh-coth method for some nonlinear pseudoparabolic equations with exact solutions, Advances in Difference Equations, 2013 (2013), 143.
18. [18] H. Holden and X. Raynaud, Global conservative solutions of the generalized hyperelastic-rod wave equation, Journal of Differential Equations, 233 (2007), 448–484.
19. [19] M. Bendahmane, G. Coclite and K. Karlsen, H1-perturbations of smooth solutions for a weakly dissipative hyperelastic-rod wave equation, Mediterranean Journal of Mathematics, 3 (2006), 419–432.
20. [20] G.M. Coclite, H. Holden and K.H. Karlsen, Global Weak Solutıons To A Generalızed Hyperelastıc-Rod Wave Equatıon, SIAM Journal on Mathematical Analysis, 37(4) (2005), 51-66.
21. [21] H.M. Srivastava, H. G¨unerhan and B. Ghanbari, Exact traveling wave solutions for resonance nonlinear Schr¨odinger equation with intermodal dispersions and the Kerr law nonlinearity, Mathematical Methods in the Applied Sciences, 42(18) (2019), 7210-7221.
22. [22] B. Ghanbari, M. S. Osman and D. Baleanu, Generalized exponential rational function method for extended Zakharov Kuzetsov equation with conformable derivative, Modern Physics Letters A, 34(20) (2019), 1950155.
23. [23] B. Ghanbari and J.F. Gomez, The generalized exponential rational function method for Radhakrishnan-Kundu-Lakshmanan equation with b-conformable time derivative, Revista Mexicana de Fisica, 65(5) (2019), 503-518.
24. [24] Y. Sag˘lam O¨ zkan, The generalized exponential rational function and Elzaki–Adomian decomposition method for the Heisenberg ferromagnetic spin chain equation, Journal of Nonlinear Science and Applications, 35(12) (2021), 2150200.
25. [25] K.K. Ali, R. Yilmazer, H. Bulut, T. Akt¨urk and M.S. Osman, Abundant exact solutions to the strain wave equation in micro-structured solids, Modern Physics Letters B, 35 (2021), 2150439.