zbMATH — the first resource for mathematics

Exact travelling wave solutions of the Schamel-Korteweg-de Vries equation. (English) Zbl 1248.35188
Summary: The Schamel-Korteweg-de Vries (S-KdV) equation containing a square root nonlinearity is a very attractive model for the study of ion-acoustic waves in plasma and dusty plasma. We obtain exact travelling wave solutions of the S-KdV equation by employing the exp function method. The work emphasizes the power of the method in providing distinct solutions of different physical problems.

35Q53 KdV equations (Korteweg-de Vries equations)
35C07 Traveling wave solutions
35C05 Solutions to PDEs in closed form
Full Text: DOI
[1] Abbasbandy, S.; Shirzadi, A., The first integral method for modified benjamin – bona – mahony equation, Commun. nonlin. science numerical simulation, 15, 7, 1759-1764, (2010) · Zbl 1222.35166
[2] Dehghan, M.; Shakeri, F., Use of He’s homotopy perturbation method for solving a partial differential equation arising in modeling of flow in porous media, J. porous media, 11, 765-778, (2008)
[3] Dehghan, M.; Manafian, J., The solution of the variable coefficients fourth-order parabolic partial differential equations by the homotopy perturbation method, Z. naturforschung A, 64a, 411-419, (2009)
[4] Das, G.C.; Tagare, S.G.; Sarma, J., Quasi-potential analysis for ion-acoustic solitary wave and double layers in plasmas, Planet. space sci., 46, 417, (1998)
[5] He, J.H.; Wu, X.H., Exp-function method for nonlinear wave equations, Chaos, solitons fractals, 30, 700-708, (2006) · Zbl 1141.35448
[6] He, J.H., Variational iteration method—a kind of non-linear analytical technique: some examples, Int. J. non-linear mech., 34, 699-708, (1999) · Zbl 1342.34005
[7] Mokhtari, R., Variational iteration method for solving nonlinear differential-difference equations, Int. J. nonlinear sci. numer. simul., 9, 19-24, (2008) · Zbl 1401.65152
[8] Sakthivel, R.; Chun, C., New soliton solutions of chaffee-infante equations, Z. naturforsch. A (J. phys. sci.), 65a, 197-202, (2010)
[9] Sakthivel, R.; Chun, C.; Lee, J., New travelling wave solutions of Burgers equation with finite transport memory, Z. naturforsch. A (J. phys. sci.), 65, 633-640, (2010)
[10] Chun, C.; Sakthivel, R., Homotopy perturbation technique for solving two-point boundary value problems- comparison with other methods, Computer phys. commun., 181, 1021-1024, (2010) · Zbl 1216.65094
[11] Chun, C.; Sakthivel, R., New soliton and periodic solutions for two nonlinear physical models, Z. naturforsch. A (J. phys. sci.), 65a, 1049-1054, (2010)
[12] Lee, J.; Sakthivel, R., Exact traveling wave solutions of a higher-dimensional nonlinear evolution equation, Mod. phys. lett. B, 24, 1011-1021, (2010) · Zbl 1188.37063
[13] Tagare, S.G.; Chakraborty, A.N., Solution of a generalised korteweg – devries equation, Phys. fluids, 17, 1331, (1974)
[14] Schamel, H., A modified korteweg – de Vries equation for ion acoustic waves due to resonant electrons, Plasma phys., 9, 377, (1973)
[15] Yusufoglu, E.; Bekir, A., The tanh and the sine-cosine methods for exact solutions of the MBBM and the Vakhnenko equations, Chaos, solitons and fractals, 38, 1126-1133, (2008) · Zbl 1152.35485
[16] Zhang, S.; Zhang, H., Exp-function method for N-soliton solutions of nonlinear evolution equations in mathematical physics, Phys. lett. A, 373, 2501-2505, (2009) · Zbl 1231.35220
[17] Zhang, S.; Zhang, H., Variable-coefficient discrete tanh method and its application to (2+1)-dimensional Toda equation, Phys. lett. A, 373, 905-2910, (2009) · Zbl 1233.37046
[18] Zhang, S., Exp-function method: solitary, periodic and rational wave solutions of nonlinear evolution equations, Nonlinear sci. lett. A, 1, 143-146, (2010)
[19] Zhang, S.; Zong, Q.A.; Liu, D.; Gao, Q., A generalized exp-function method for fractional Riccati differential equations, Commun. fractal calculus, 1, 48-51, (2010)
[20] Yildirim, A.; Agirseven, D., The homotopy perturbation method for solving singular initial value problems, Int. J. nonlinear sci. numer. simul., 10, 235-238, (2009)
[21] Hosseini, H.; Kabir, M.M.; Khajeh, A., New explicit solutions for the Vakhnenko and a generalized form of the nonlinear heat conduction equations via exp-function method, Int. J. nonlinear sci. numer. simul., 10, 1307-1318, (2009)
[22] Mohyud-Din, S.T.; Noor, M.A.; Noor, K.I., Variational iteration method for re-formulated partial differential equations, Internat. J. nonlinear sci. numer., 11, 87-92, (2010) · Zbl 1401.65141
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.