
AIMS Mathematics, 2019, 4(6): 15231539. doi: 10.3934/math.2019.6.1523
Research article Special Issues
Export file:
Format
 RIS(for EndNote,Reference Manager,ProCite)
 BibTex
 Text
Content
 Citation Only
 Citation and Abstract
New solitary wave solutions and stability analysis of the BenneyLuke and the Phi4 equations in mathematical physics
1 Department of Engineering Science, Kermanshah University of Technology, Kermanshah, Iran
2 Firat University, Science Faculty, Department of Mathematics, 23119 Elazig, Turkey
3 Federal University Dutse, Science Faculty, Department of Mathematics, 7156 Dutse, Nigeria
4 Cankaya University, Science Faculty, Department of Mathematics, 06530 Ankara, Turkey
5 Institute of Space Sciences, Magurele, Romania
Received: , Accepted: , Published:
Special Issues: Recent Advances in Fractional Calculus with Real World Applications
References
1. M. J. Ablowitz and P. A. Clarkson, Solitons, Nonlinear Evolution Equations and Inverse Scattering Transform, Cambridge University Press, Cambridge, 1990.
2. F. Tchier, A. I. Aliyu, A. Yusuf, et al. Dynamics of solitons to the illposed Boussinesq equation, Eur. Phys. J. Plus, 132 (2017), 136.
3. F. Tchier, A. Yusuf, A. I. Aliyu, et al. Soliton solutions and conservation laws for lossy nonlinear transmission line equation, Superlattices Microstruct, 107 (2017), 320336.
4. W. X. Ma, A soliton hierarchy associated with so (3,R), Appl. Math. Comput., 220 (2013), 117122.
5. E. Bas, B. Acay, R. Ozarslan, The price adjustment equation with different types of conformable derivatives in market equilibrium, AIMS Mathematics, 4 (2019), 805820.
6. B. Acay, E. Bas, T. Abdeljawad, Nonlocal fractional calculus from different viewpoint generated by truncated Mderivative, J. Comput. Appl. Math., 366 (2020), 112410.
7. S. Ali, M. Younis, M. O. Ahmad, et al. Rogue wave solutions in nonlinear optics with coupled Schrodinger equations, Opt. Quant. Electron., 50 (2018), 266.
8. N. Raza, I. G. Murtaza, S. Sial, et al. On solitons: the biomolecular nonlinear transmission line models with constant and time variable coefficients, Wave. Random Complex, 28 (2018), 553569.
9. M. Younis, S. T. R. Rizvi, S. Ali, Analytical and soliton solutions: Nonlinear model of nanobioelectronics transmission lines, Appl. Math. Comput., 265 (2015), 9941002.
10. S. Ali, S. T. R. Rizvi, M. Younis, Traveling wave solutions for nonlinear dispersive waterwave systems with timedependent coefficients, Nonlinear Dynam., 82 (2015), 17551762.
11. B. Younas, M. Younis, M. O. Ahmed, et al. Chirped optical solitons in nanofibers, Mod. Phys. Lett. B, 32 (2018), 1850320.
12. K. Ali, S. T. R. Rizvi, A. Khalil, et al. Chirped and dipole soliton in nonlinear negativeindex materials, Optik, 172 (2018), 657661.
13. K. U. Tariq, M. Younis, Bright, dark and other optical solitons with second order spatiotemporal dispersion, Optik, 142 (2017), 446450.
14. M. Younis, Optical solitons in (n+1) dimensions with Kerr and power law nonlinearities, Mod. Phys. Lett. B, 31 (2017), 1750186.
15. M. Younis, U. Younas, S. ur Rehman, et al. Optical brightdark and Gaussian soliton with third order dispersion, Optik, 134 (2017), 233238.
16. E. Bas, B. Acay, R. Ozarslan, Fractional models with singular and nonsingular kernels for energy efficient buildings, Chaos, 29 (2019), 023110.
17. J. H. He, Variational principles for some nonlinear partial differential equations with variable coefficients, Chaos, Solitons and Fractals, 19 (2004), 847851.
18. G. Adomian, Solving Frontier Problems of Physics: The Decomposition Method, Kluwer Academic Publishers, Boston, 1994.
19. K. Khan, M. A. Akbar, Exact and solitary wave solutions for the TzitzeicaDoddBullough and the modified KdVZakharovKuznetsov equations using the modified simple equation method, Ain Shams Eng. J., 4 (2013), 903909.
20. K. Khan, M. A. Akbar, Traveling wave solutions of the (2+1)dimensional Zoomeron equation and the Burgers equations via the MSE method and the Expfunction method, Ain Shams Eng. J., 5 (2014), 247256.
21. A. Bekir, A. Boz, Exact solutions for nonlinear evolution equation using Expfunction method, Phys. Lett. A, 372 (2008), 16191625.
22. H. O. Roshid, N. Rahman, M. A. Akbar, Traveling waves solutions of nonlinear Klein Gordon equation by extended (G/G)expasion method, Ann. Pure Appl. Math., 3 (2013), 1016.
23. A. Javid, N. Raza, M. S. Osman, Multisolitons of Thermophoretic Motion Equation Depicting the Wrinkle Propagation in SubstrateSupported Graphene Sheets, Commun. Theor. Phys., 71 (2019), 362.
24. M. S. Osman, Onesoliton shaping and inelastic collision between double solitons in the fifthorder variablecoefficient SawadaKotera equation, Nonlinear Dyn., 96 (2019), 14911496.
25. M. S. Osman, New analytical study of water waves described by coupled fractional variant Boussinesq equation in fluid dynamics, PramanaJ. Phys., 93 (2019), 26.
26. M. S. Osman, D. Lu, M. M. A. Khater, et al. Complex wave structures for abundant solutions related to the complex GinzburgLandau model, Optik, 192 (2019), 162927.
27. D. Lu, K. U. Tariq, M. S. Osman, et al. New analytical wave structures for the (3 + 1)dimensional KadomtsevPetviashvili and the generalized Boussinesq models and their applications, Results phys., 14 (2019), 102491.
28. H. I. AbdelGawad, N. S. Elazab, M. Osman, Exact Solutions of Space Dependent Kortewegde Vries Equation by The Extended Unified Method, J. Phys. Soc. Jpn, 82 (2013), 044004.
29. M. Osman, Multisoliton rational solutions for some nonlinear evolution equations, Open Phys., 14 (2016), 2636.
30. H. I. AbdelGawad and M. Osman, On shallow water waves in a medium withtimedependent dispersion and nonlinearitycoefficients, J. Adv. Res., 6 (2015), 593599.
31. B. Ghanbari, M. S. Osman, D. Baleanu, Generalized exponential rational function method for extended ZakharovKuzetsov equation with conformable derivative, Mod. Phys. Lett. A, 34 (2019), 1950155.
32. M. S. Osman, A. M. Wazwaz, A general bilinear form to generate different wave structures of solitons for a (3+1)dimensional BoitiLeonMannaPempinelli equation, Mathematical Methods in the Applied Sciences.
33. U. Khan, R. Ellahi, R. Khan, et al. Extracting new solitary wave solutions of BennyLuke equation and Phi4 equation of fractional order by using (G'/G)expansion method, Opt. Quant. Electron., 49 (2017), 362.
34. B. Ghanbari, M. Inc, A new generalized exponential rational function method to find exact special solutions for the resonance nonlinear Schrödinger equation, Eur. Phys. J. Plus, 133 (2018), 142.
35. M. Saha, A. K. Sarma, Solitary wave solutions and modulation instability analysis of the nonlinear Schrodinger equation with higher order dispersion and nonlinear terms, Commun. Nonlinear Sci. Numer. Simulat., 18 (2013), 24202425.
36. A. R. Seadawy, M. Arshad, D. Lu, Stability analysis of new exact traveling wave solutions of new coupled KdV and new coupled ZakharovKuznetsov systems, Eur. Phys. J. Plus, 132 (2017), 162.
37. M. Inc, A. Yusuf, A. I. Aliyu, et al. Soliton solutions and stability analysis for some conformable nonlinear partial differential equations in mathematical physics, Opt. Quant. Electron., 50 (2018), 190.
© 2019 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)