References
1. Jawad, A.J.M., Petkovic, M.D., Laketa, P., and
Biswas, A. \Dynamics of shallow water waves with
Boussinesq equation", Scientia Iranica, Trans. B,
20(1), pp. 179-184 (2013).
2. Karakoc, S.B.G., Zeybek, H. and Ak, T. \Numerical
solutions of the Kawahara equation by the septic Bspline
collocation method", Statistics, Optimization
and Information Computing, 2, pp. 211-221 (2014).
3. Girgis, L., Zerrad, E. and Biswas, A. \Solitary wave
solutions of the Peregrine equation", International
Journal of Oceans and Oceanography, 4(1), pp. 45-54
(2010).
4. Biswas, A. \1-Soliton solution of Benjamin-Bona-
Mahony equation with dual-power law nonlinearity",
Communications in Nonlinear Science and Numerical
Simulation, 15(10), pp. 2744-2746 (2010).
5. Saka, B. \Quintic B-spline collocation method for numerical
solution of the RLW equation", The ANZIAM
Journal, 49(3), pp. 389-410 (2008).
6. Korkmaz, A. \Numerical algorithms for solutions of
Korteweg-de Vries equation", Numerical Methods for
Partial Di erential Equations, 26(6), pp. 1504-1521
(2009).
7. Biswas, A., Krishnan, E.V., Suarez, P., Kara, A.H.
and Kumar, S. \Solitary waves and conservation law
2596 T. Ak et al./Scientia Iranica, Transactions B: Mechanical Engineering 25 (2018) 2582{2597
of Bona-Chen equation", Indian Journal of Physics,
87(2), pp. 169-175 (2013).
8. Triki, H., Kara, A.H., Bhrawy, A., and Biswas,
A. \Soliton solution and conservation law of Gear-
Grimshaw model for shallow water waves", Acta Physica
Polonica A, 125(5), pp. 1099-1106 (2014).
9. Osman, M.S. \Multi-soliton rational solutions for
quantum Zakharov-Kuznetsov equation in quantum
magnetoplasmas", Waves in Random and Complex
Media, 26(4), pp. 434-443 (2016).
10. Osman, M.S. \Multiwave solutions of time-fractional
(2 + 1)-dimensional Nizhnik Novikov Veselov equations",
Pramana Journal of Physics, 88(4), 67 (2017).
11. Osman, M.S. \Nonlinear interaction of solitary waves
described by multi-rational wave solutions of the (2 +
1)-dimensional Kadomtsev-Petviashvili equation with
variable coecients", Nonlinear Dynamics, 87(2), pp.
1209-1216 (2017).
12. Osman, M.S. \Analytical study of rational and doublesoliton
rational solutions governed by the KdVSawada-
Kotera-Ramani equation with variable coef-
cients", Nonlinear Dynamics, 89(3), pp. 2283-2289
(2017).
13. Youssri, Y.H. \A new operational matrix of Caputo
fractional derivatives of Fermat polynomials: an
application for solving the Bagley-Torvik equation",
Advances in Di erence Equations, 73, pp. 1-17 (2017).
14. Sohail, A., Siddiqui, A.M. and Iftikhar, M. \Travelling
wave solutions for fractional order KdV-like equations
using G0=G-expansion", Nonlinear Science Letters A,
8(2), pp. 228-235 (2017).
15. Sohail, A., Rees, J.M. and Zimmerman, W.B. \Analysis
of capillary-gravity waves using the discrete periodic
inverse scattering transform", Colloids and Surfaces A:
Physicochemical and Engineering Aspects, 391(1), pp.
42-50 (2011).
16. Zeybek, H. and Karakoc, S.B.G. \A numerical investigation
of the GRLW equation using lumped Galerkin
approach with cubic B-spline", SpringerPlus, 5(199),
pp. 1-17 (2016).
17. Ak, T., Karakoc, S.B.G. and Biswas, A. \A new
approach for numerical solution of modi ed Kortewegde
Vries equation", Iranian Journal of Science
and Technology, Transactions A: Science (2017).
doi.org/10.1007/s40995-017-0238-5
18. Ak, T., Karakoc, S.B.G., and Biswas, A. \Application
of Petrov-Galerkin method to shallow water waves
model: Modi ed Korteweg-de Vries equation", Scientia
Iranica B, 24(3), pp. 1148-1159 (2017).
19. Karakoc, S.B.G. and Zeybek, H. \Solitary wave solutions
of the GRLW equation using septic B-spline
collocation method", Applied Mathematics and Computation,
289, pp. 159-171 (2016).
20. Triki, H., Ak, T., Moshokoa, S.P., and Biswas,
A. \Soliton solutions to KdV equation with spatiotemporal
dispersion", Ocean Engineering, 114, pp.
192-203 (2016).
21. Yagmurlu, N.M., Tasbozan, O., Ucar, Y., and Esen,
A. \Numerical solutions of the combined KdV-mKdV
equation by a quintic B-spline collocation method",
Applied Mathematics & Information Sciences Letters,
4(1), pp. 19-24 (2016).
22. Ak, T., Triki, H., and Biswas, A. \Numerical simulation
for treatment of dispersive shallow water waves
with Rosenau-KdV equation", The European Physical
Journal Plus, 131(10), pp. 356-370 (2016).
23. Triki, H., Ak, T., and Biswas, A. \New types of solitonlike
solutions for a second order wave equation of
Korteweg-de Vries type", Applied and Computational
Mathematics, 16(2), pp. 168-176 (2017).
24. Triki, H., Ak, T., Ekici, M., Sonmezoglu, A., Mirzazadeh,
M., Kara, A.H., and Aydemir, T. \Some new
exact wave solutions and conservation laws of potential
Korteweg-de Vries equation", Nonlinear Dynamics,
89(1), pp. 501-508 (2017).
25. Abd-Elhameed, W.M. and Youssri, Y.H. \Spectral solutions
for fractional di erential equations via a novel
Lucas operational matrix of fractional derivatives",
Romanian Journal of Physics, 61(5-6), pp. 795-813
(2016).
26. Abd-Elhameed, W.M. and Youssri, Y.H. \Generalized
Lucas polynomial sequence approach for fractional
di erential equations", Nonlinear Dynamics, 89(2),
pp. 1341-1355 (2017).
27. Marchant, T.R. \Asymptotic solitons for a higherorder
modi ed Korteweg-de Vries equation", Physical
Review E, 66(046623), pp. 1-8 (2002).
28. Marchant, T.R. \Asymptotic solitons for a thirdorder
Korteweg-de Vries equation", Chaos, Solitons &
Fractals, 22, pp. 261-270 (2004).
29. Je rey, A. and Kakutani, T. \Weak nonlinear dispersive
waves: A discussion centered around the
Korteweg-de Vries equation", SIAM Review, 14(4), pp.
582-643 (1972).
30. Canivar, A., Sari, M., and Dag, I. \A Taylor-Galerkin
nite element method for the KdV equation using cubic
B-splines", Physica B, 405, pp. 3376-3383 (2010).
31. Dag, I. and Dereli, Y. \Numerical solutions of KdV
equation using radial basis functions", Applied Mathematical
Modelling, 32(4), pp. 535-546 (2008).
32. Saka, B. \Cosine expansion-based di erential quadrature
method for numerical solution of the KdV equation",
Chaos, Solitons & Fractals, 40(5), pp. 2181-2190
(2009).
33. Ersoy, O. and Dag, I. \The exponential cubic B-spline
algorithm for Korteweg-de Vries equation", Advances
in Numerical Analysis, 2015, Article ID 367056, 8
pages (2015).
T. Ak et al./Scientia Iranica, Transactions B: Mechanical Engineering 25 (2018) 2582{2597 2597
34. Soliman, A.A. \Collocation solution of the Kortewegde
Vries equation using septic splines", International
Journal of Computer Mathematics, 81(3), pp. 325-331
(2004).
35. Zaki, S.I. \A quintic B-spline nite elements scheme
for the KdVB equation", Computer Methods in Applied
Mechanics and Engineering, 188, pp. 121-134 (2000).
36. Antonova, M. and Biswas, A. \Adiabatic parameter
dynamics of perturbed solitary waves", Communications
in Nonlinear Science and Numerical Simulation,
14(3), pp. 734-748 (2009).
37. Suli, A. and Mayers D.F., An Introduction to Numerical
Analysis, Cambridge University Press, Cambridge,
England (2003).
38. Prenter, P.M., Splines and Variational Methods, John
Wiley, New York, USA (1975).
39. Bochev, P.B. and Gunzburger, M.D., Least-Squares
Finite Element Methods, Springer, New York, USA
(2009).
40. Thomee, V., Galerkin Finite Element Methods for
Parabolic Problems, Springer, Berlin, Germany (2006).
41. Dhawan, S., Bhowmik, S.K., and Kumar, S. \Galerkinleast
square B-spline approach toward advectiondi
usion equation", Applied Mathematics and Computation,
261, pp. 128-140 (2015).
42. Berezin, Y.A. and Karpman, V.I. \Nonlinear evolution
of disturbances in plasma and other dispersive media",
Soviet Physics JETP, 24, pp. 1049-1056 (1967).
)
