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Homotopy analysis method for the Kawahara equation. (English) Zbl 1181.35224
Summary: The homotopy analysis method (HAM) is used to find a family of travelling-wave solutions of the Kawahara equation. This approximate solution, which is obtained as a series of exponentials, has a reasonable residual error. The homotopy analysis method contains the auxiliary parameter \(\hbar\), which provides us with a simple way to adjust and control the convergence region of series solution. This method is reliable and manageable.

MSC:
35Q53 KdV equations (Korteweg-de Vries equations)
35C07 Traveling wave solutions
35C10 Series solutions to PDEs
35A20 Analyticity in context of PDEs
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[1] Liao, S.J., Beyond perturbation: introduction to the homotopy analysis method, (2003), Chapman & Hall/CRC Press Boca Raton
[2] Abbasbandy, S., Phys. lett. A, 360, 109, (2006)
[3] Abbasbandy, S., Phys. lett. A, 361, 478, (2007) · Zbl 1273.65156
[4] Allan, F.M., Appl. math. comput., 190, 6, (2007)
[5] Sajid, M.; Hayat, T.; Asghar, S., Comparison between the HAM and HPM solutions of thin film flows of non-Newtonian fluids on a moving belt, Nonlinear dynam., 50, 27, (2007) · Zbl 1181.76031
[6] Abbasbandy, S., Int. commun. heat mass, 34, 380, (2007)
[7] Abbasbandy, S.; Samadian Zakaria, F., Nonlinear dynam., 51, 83, (2008)
[8] Abbasbandy, S.; Angew, Z., Math. phys. (ZAMP), 59, 51, (2008)
[9] Liao, S.J., Int. J. heat mass transfer, 48, 2529, (2005)
[10] Liao, S.J., Stud. appl. math., 117, 239, (2006)
[11] Liao, S.J.; Magyari, E.; Angew, Z., Math. phys. (ZAMP), 57, 777, (2006)
[12] Liao, S.J.; Su, J.; Chwang, A.T., Int. J. heat mass transfer, 49, 2437, (2006)
[13] Tan, Y.; Xu, H.; Liao, S.J., Chaos, solitons fractals, 31, 462, (2007)
[14] Wu, W.; Liao, S.J., Chaos, solitons fractals, 26, 177, (2005)
[15] Hayat, T.; Sajid, M., Phys. lett. A, 361, 316, (2007) · Zbl 1170.76307
[16] Hayat, T.; Khan, M., Nonlinear dynam., 42, 395, (2005)
[17] Hayat, T.; Khan, M.; Ayub, M.; Angew, Z., Math. phys. (ZAMP), 56, 1012, (2005)
[18] Sajid, M.; Hayat, T.; Asghar, S., Phys. lett. A, 355, 18, (2006)
[19] Tan, Y.; Abbasbandy, S., Commun. nonlinear sci. numer. simul., 13, 539, (2008)
[20] Wang, C., Heat mass. transfer., 42, 759, (2006)
[21] Abbasbandy, S., Appl. math. model., 32, 2706, (2008)
[22] Hayat, T.; Sajid, M.; Pop, I., Three-dimensional flow over a stretching surface in a viscoelastic fluid, Nonlinear anal. RWA, 9, 1811, (2008) · Zbl 1154.76315
[23] Wazwaz, A.M., Appl. math. comput., 182, 1642, (2006)
[24] Kawahara, T., J. phys. soc. Japan, 33, 260, (1972)
[25] Sirendaoreji, S.J., Chaos, solitons fractals, 19, 147, (2004)
[26] Kaya, D.; Al-Khaled, K., Phys. lett. A, 363, 433, (2007)
[27] Yusufoglu, E.; Bekir, A.; Alp, M., Periodic and solitary wave solutions of Kawahara and modified Kawahara equations by using sine-cosine method, Chaos, solitons fractals, 37, 1193, (2008) · Zbl 1148.35351
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