References
- T. Ak, S.B.G. Karakoc and A. Biswas. Numerical simulation of dispersive shallow water waves with an efficient method. Journal of Computational and Theoretical Nanoscience, 12(12):5995–6001, 2015. https://doi.org/10.1166/jctn.2015.4748.
- T. Ak, S.B.G. Karakoc and H. Triki. Numerical simulation for treatment of dispersive shallow water waves with Rosenau-KdV equation. The European Physical Journal Plus, 131(10):356–370, 2016. https://doi.org/10.1140/epjp/i2016-16356-3.
- A. Biswas, H. Triki and M. Labidi. Bright and dark solitons of the RosenauKawahara equation with power law nonlinearity. Physics of Wave Phenomena, 19(1):24–29, 2011. https://doi.org/10.3103/S1541308X11010067.
- P.B. Bochev and M.D. Gunzburger. Least-squares finite element methods. Springer, New York, 2009.
- H. Demiray. Higher order approximations in reductive perturbation methods: strongly dispersive waves. Communications in Nonlinear Science and Numerical Simulation, 10(5):549–558, 2005. https://doi.org/10.1016/j.cnsns.2003.08.004.
- A. Esfahani. Solitary wave solutions for generalized Rosenau-KdV equation. Communications in Theoretical Physics, 55(3):396–398, 2011. https://doi.org/10.1088/0253-6102/55/3/04.
- J. Hu, Y. Xu and B. Hu. Conservative linear difference scheme for Rosenau-KdV equation. Advances in Mathematical Physics, 2013:1–7, 2013. https://doi.org/10.1155/2013/423718.
- S.B.G. Karakoc and T. Ak. Numerical simulation of dispersive shallow water waves with Rosenau-KdV equation. Internatioal Journal of Advances in Applied Mathematics and Mechanics, 3(3):32–40, 2016.
- S.B.G. Karakoc and T. Ak. Numerical solution of Rosenau-KdV equation using subdomain finite element method. New Trends in Mathematical Sciences, 4(1):223–235, 2016. https://doi.org/10.20852/ntmsci.2016115857.
- D.J. Korteweg and G. de Vries. XLI. on the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary wave. Philosophical Magazine Series 5, 39(240):422–443, 1895. https://doi.org/10.1080/14786449508620739.
- P.M. Prenter. Splines and variational methods. John Wiley, New York, 1975.
- P. Razborova, B. Ahmed and A. Biswas. Solitons, shock waves and conservation laws of Rosenau-KdV-RLW equation with power law nonlin-earity. Applied Mathematics & Information Sciences, 8(2):485–491, 2014. https://doi.org/10.12785/amis/080205.
- P. Razborova, A.H. Kara and A. Biswas. Additional conservation laws for Rosenau-KdV-RLW equation with power law nonlinearity by Lie symmetry. Nonlinear Dynamics, 79(1):743–748, 2015. https://doi.org/10.1007/s11071-014-1700-y.
- P. Razborova, L. Moraru and A. Biswas. Perturbation of dispersive shallow water waves with Rosenau-KdV-RLW equation with power law nonlinearity. Romanian Journal of Physics, 59(7-8):658–676, 2014.
- P. Razborova, H. Triki and A. Biswas. Perturbation of dispersive shallow water waves. Ocean Engineering, 63:1–7, 2013. https://doi.org/10.1016/j.oceaneng.2013.01.014.
- P. Rosenau. A quasi-continuous description of a nonlinear transmission line. Physica Scripta, 34(6B):827–829, 1986. https://doi.org/10.1088/0031- 8949/34/6b/020.
- P. Rosenau. Dynamics of dense discrete systems. Progress of Theoretical Physics, 79(5):1028–1042, 1988. https://doi.org/10.1143/PTP.79.1028.
- A. Saha. Topological 1-soliton solutions for the generalized Rosenau-KdV equation. Fundamental Journal Mathematical Physics, 2(1):19–25, 2012.
- P. Sanchez, G. Ebadi, A. Mojaver, M. Mirzazadeh, M. Eslami and A. Biswas. Solitons and other solutions to perturbed Rosenau-KdV-RLW equation with power law nonlinearity. Acta Physica Polonica A, 127(6):1577–1586, 2015. https://doi.org/10.12693/APhysPolA.127.1577.
- E. Süli and D.F. Mayers. An introduction to numerical analysis. Cambridge University Press, Cambridge, 2003. https://doi.org/10.1017/CBO9780511801181.
- V. Thomee. Galerkin finite element methods for parabolic problems. SpringerVerlag, Berlin, 2006.
- H. Triki, T. Ak, S.P. Moshokoa and A. Biswas. Soliton solutions to KdV equation with spatio-temporal dispersion. Ocean Engineering, 114:192–203, 2016. https://doi.org/10.1016/j.oceaneng.2016.01.022.
- B. Wongsaijai and K. Poochinapan. A three-level average implicit finite difference scheme to solve equation obtained by coupling the Rosenau-KdV equation and the Rosenau-RLW equation. Applied Mathematics and Computation, 245:289–304, 2014. https://doi.org/10.1016/j.amc.2014.07.075.
- M. Zheng and J. Zhou. An average linear difference scheme for the generalized Rosenau-KdV equation. Journal of Applied Mathematics, 2014:1–9, 2014. https://doi.org/10.1155/2014/202793.
- J.-M. Zuo. Solitons and periodic solutions for the Rosenau-KdV and RosenauKawahara equations. Applied Mathematics and Computation, 215(2):835–840, 2009. https://doi.org/10.1016/j.amc.2009.06.011.