zbMATH — the first resource for mathematics

Exact and numerical solitary wave solutions of generalized Zakharov equation by the Adomian decomposition method. (English) Zbl 1130.35120
Summary: Exact and numerical solutions are calculated for the generalized Zakharov equation, which is an imaginary equation, with initial condition by considering the modified Adomian decomposition method (mADM). The method does not need linearization, weak nonlinearity assumptions or perturbation theory. We compare the numerical solutions with corresponding analytical solutions.

35Q55 NLS equations (nonlinear Schrödinger equations)
35A25 Other special methods applied to PDEs
35Q51 Soliton equations
76M25 Other numerical methods (fluid mechanics) (MSC2010)
Full Text: DOI
[1] Zakharov, V.E., Collapse of Langmuir waves, Zh eksp teor fiz, 62, 1745-1751, (1972)
[2] Goldman, M.V., Langmuir wave solitons and spatial collapse in plasma physics, Physica D, 18, 67-76, (1986) · Zbl 0613.76129
[3] Nicholson, D.R., Introduction to plasma theory, (1983), Wiley New York
[4] Li, L.H., Langmuir turbulence equations with the self-generated magnetic field, Phys fluids B, 5, 350-356, (1993)
[5] Malomed, B.; Anderson, D.; Lisak, M.; Quiroga-Teixeiro, M.L., Dynamics of solitary waves in the Zakharov model equations, Phys rev E, 55, 962-968, (1997)
[6] Vakhnenko, V.O.; Parkes, E.J.; Morrison, A.J., A Bäcklund transformation and the inverse scattering transform method for the generalised Vakhnenko equation, Chaos, solitons & fractals, 17, 683-692, (2003) · Zbl 1030.37047
[7] Sun, Y.-p.; Bi, J.-b.; Chen, D.-y., N-soliton solutions and double Wronskian solution of the non-isospectral AKNS equation, Chaos, solitons & fractals, 26, 905-912, (2005) · Zbl 1093.35056
[8] Sakka, A., Bäcklund transformations for painleve I and II equations to painleve-type equations of second order and higher degree, Phys lett A, 300, 228-232, (2002) · Zbl 0997.34082
[9] Yao, R.-x.; Li, Z.-b., New exact solutions for three nonlinear evolution equations, Phys lett A, 297, 196-204, (2002) · Zbl 0995.35003
[10] Zhang, J.-f.; Lai, X.-j., A class of periodic solutions of (2+1)-dimensional Boussinesq equation, J phys soc jpn, 73, 2402-2410, (2004)
[11] Liu, Z.; Chen, C., Compactons in a general compressible hyperelastic rod, Chaos, solitons & fractals, 22, 627-640, (2004) · Zbl 1116.74374
[12] Kaya, D.; El-Sayed, S.M., An application of the decomposition method for the generalized KdV and RLW equations, Chaos, solitons & fractals, 17, 869-877, (2003) · Zbl 1030.35139
[13] El-Danaf, T.S.; Ramadan, M.A.; Abd Alaal, F.E.I., The use of Adomian decomposition method for solving the regularized long-wave equation, Chaos, solitons & fractals, 26, 747-757, (2005) · Zbl 1073.35010
[14] Kaya, D.; El-Sayed, S.M., On the solution of the coupled schröndinger-KdV equation by the decomposition method, Phys lett A, 313, 82-88, (2003) · Zbl 1040.35099
[15] Wazwaz AM. The modified decomposition method for analytic treatment of differential equations. Appl Math Comput, in press.
[16] Babolian, E.; Javadi, Sh., New method for calculating Adomian polynomials, Appl math comput, 153, 253-259, (2004) · Zbl 1055.65068
[17] Zhu, Y.; Chang, Q.; Wu, S., A new algorithm for calculating Adomian polynomials, Appl math comput, 169, 402-416, (2005) · Zbl 1087.65528
[18] Wang, M.; Li, X., Extended F-expansion method and periodic wave solutions for the generalized Zakharov equations, Phys lett A, 343, 48-54, (2005) · Zbl 1181.35255
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.