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To construct the infinite sequence new exact solutions of nonlinear evolution equations and study the first kind of elliptic function, new solutions and the corresponding Bäcklund transformation of the equation are presented. Based on this, the generalized pentavalent KdV equation and the breaking soliton equation are chosen as applicable examples and infinite sequence smooth soliton solutions, infinite sequence peak solitary wave solutions and infinite sequence compact soliton solutions are obtained with the help of symbolic computation system Mathematica. The method is of significance to search for infinite sequence new exact solutions to other nonlinear evolution equations. 相似文献
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Starting from a simple transformation, and with the aid of symbolic computation, we establish the relation- ship between the solution of a generalized variable coefficient Kadomtsev-Petviashvili (vKP) equation and the solution of a system of linear partial differential equations. According to this relation, we obtain Wronskian form solutions of the vKP equation, and further present N-soliton-like solutions for some degenerated forms of the vKP equation. Moreover, we also discuss the influences of arbitrary constants on the soliton and N-soliton solutions of the KPII equation. 相似文献
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Fusion,fission, and annihilation of complex waves for the (2+l)-dimensional generalized Calogero-Bogoyavlenskii-Schiff system 下载免费PDF全文
With the help of the symbolic computation system, Maple and Riccati equation (ξ' = ao + a1ξ+ a2ξ2), expansion method, and a linear variable separation approach, a new family of exact solutions with q = lx + my + nt + Г(x,y, t) for the (2+1)-dimensional generalized Calogero-Bogoyavlenskii-Schiff system (GCBS) are derived. Based on the derived solitary wave solution, some novel localized excitations such as fusion, fission, and annihilation of complex waves are investigated. 相似文献
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基于Bell多项式,构造了获得非线性发展方程双线性形式的一个新算法,并且开发了相应的程序包.非线性发展方程与其双线性形式之间的变换可由该程序包自动推导,同时给出了一些具有代表性的实例验证了该程序包的有效性与可靠性. 相似文献
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