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1.
New solitons and kink solutions for the Gardner equation 总被引:3,自引:1,他引:2
The Gardner equation, also called combined KdV–mKdV equation, is studied. New hyperbolic ansatze are proposed to derive solitons solutions. The tanh method is used as well to obtain kink solutions. 相似文献
2.
Abdul-Majid Wazwaz 《Journal of mathematical chemistry》2014,52(2):613-626
In this paper, we establish the Volterra integro-differential forms of the Lane–Emden equations. We use the variational iteration method (VIM) to effectively treat these forms. The Volterra integro-differential forms of the Lane–Emden equations overcome the singular behavior at the origin $x=0$ and do not use a variety of Lagrange multipliers. Several numerical examples are examined to show the validity of the integro-differential forms. 相似文献
3.
Abdul-Majid Wazwaz 《Central European Journal of Physics》2012,10(4):1013-1017
In this work, we explore more applications of the simplified form of the bilinear method to the seventhorder Caudrey-Dodd-Gibbon (CDG) and the Caudrey-Dodd-Gibbon-KP (CDG-KP) equation. We formally derive one and two soliton solutions for each equation. We also show that the two equations do not show resonance. 相似文献
4.
Abdul‐Majid Wazwaz Randolph Rach Jun‐Sheng Duan 《Mathematical Methods in the Applied Sciences》2014,37(1):10-19
In this paper, we introduce systems of Volterra integral forms of the Lane–Emden equations. We use the systematic Adomian decomposition method to handle these systems of integral forms. The Volterra integral forms overcome the singular behavior at the origin x = 0. The Adomian decomposition method gives reliable algorithm for analytic approximate solutions of these systems. Our results are supported by investigating several numerical examples. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
5.
Abdul-Majid Wazwaz 《Applied mathematics and computation》2011,217(21):8840-8845
A variety of shallow water waves equations in (1 + 1) and (2 + 1) dimensions are investigated. We first show that these models are completely integrable. We next determine multiple-soliton solutions for each equation. The simplified Hirota’s bilinear method developed by Hereman will be employed to achieve this goal. A comparison between dispersion relations and the phase shifts will be conducted. (But possess the same coefficients for the polynomials of exponentials.) 相似文献
6.
In this work, the completely integrable sixth-order nonlinear Ramani equation and a coupled Ramani equation are studied. Multiple soliton solutions and multiple singular soliton solutions are formally derived for these two equations. The Hirota’s bilinear method is used to determine the two distinct structures of solutions. The resonance relations for the three cases are investigated. 相似文献
7.
Abdul-Majid Wazwaz 《Applied mathematics and computation》2010,216(4):1304-1309
In this work, a combined form of the Laplace transform method with the Adomian decomposition method is developed for analytic treatment of the nonlinear Volterra integro-differential equations. The combined method is capable of handling both equations of the first and second kind. Illustrative examples will be examined to support the proposed analysis. 相似文献
8.
Abdul‐Majid Wazwaz 《Mathematical Methods in the Applied Sciences》2013,36(13):1760-1767
We derive a new ( 2 + 1)‐dimensional Korteweg–de Vries 4 (KdV4) equation by using the recursion operator of the KdV equation. This study shows that the new KdV4 equation possess multiple soliton solutions the same as the multiple soliton solutions of the KdV hierarchy, but differ only in the dispersion relations. We also derive other traveling wave solutions. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
9.
Nonlinear Dynamics - A variety of negative-order integrable modified KdV (mKdV) equations of higher orders is constructed. The inverse profile of the recursion operator of the modified KdV equation... 相似文献
10.