共查询到19条相似文献,搜索用时 109 毫秒
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根据截断的Painlevé分析展开法及相容Riccati展开(CRE)法,研究了(2+1)维广义破裂孤子方程的非局域对称.利用非局域对称局域化的方法,得到了与Schwarzian变量相对应的对称群.同时,证明了这个方程是CRE可积的,并给出了它的孤立波与椭圆周期波之间的相互作用解. 相似文献
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KdV-Burgers方程的对称与孤子解 总被引:1,自引:0,他引:1
考虑KdV-Burgers方程的一些简单对称及其构成的李代数,并利用对称约化方法将KdV-Burgers方程化为常微分方程,从而得到该方程的群不变解.此外,利用多项式展开式的方法去获得KdV-Burgers方程的新的孤子波解. 相似文献
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利用直接法将柱KdV方程超对称化.通过适当的变换,利用双线性方法将超对称柱KdV方程双线性化,由超对称Hirota双线性导数法构造出超对称柱KdV方程的单孤子解、双孤子解、三孤子解以及n孤子解的具体表达形式. 相似文献
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通过两种方法构造了一种(3+1)维高维孤子方程的孤子解.第一种方法是利用对数函数变换,将其化成双线性形式的方程,在用级数扰动法求解双线性方程的单孤子解、双孤子解和N-孤子解.第二种方法是用广义有理多项式与试探法相结合,构造了(3+1)维高维孤子方程的怪波解. 相似文献
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《高校应用数学学报(A辑)》2020,(2)
利用符号计算软件Maple,研究了几类非线性数学物理方程的精确解.由Hirota双线性方法构造了可积非局部离散mKdV方程的N-孤子解的显式表达式,且对于2-孤子解,分析了渐近行为.从Jacobi椭圆函数出发,得到了多分量Klein-Gordon方程和长波-短波方程的行波解.当模m→1,这些解退化为相应的双曲函数解,如钟型孤子解. 相似文献
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夏鸿鸣 《纯粹数学与应用数学》2013,(6):577-581
研究了(2+1)维KP方程的孤子解问题.应用Riccati方程映射法,得到了(2+1)维KP方程的新的显式精确解的结构.根据得到的精确解结构,构造出了该方程的三类精确解. 相似文献
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The symmetry of the (3 + 1)-dimensional partial differential equation has been derived via a direct symmetry method and proved to be infinite dimensional non-Virasoro type symmetry algebra. Many kinds of symmetry reductions have been obtained, including the (2 + 1)-dimensional ANNV equation and breaking soliton equation. And some new soliton solutions and complex solutions are obtained due to the Riccati equation method and symbolic computation. 相似文献
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Abdul-Majid Wazwaz 《Applied mathematics and computation》2010,217(8):4282-4288
In this work, two generalized breaking soliton equations, namely, the Bogoyavlenskii’s breaking soliton equation and its extended form, are examined. The complete integrability of these equation are justified. Multiple soliton solutions and multiple singular soliton solutions are formally derived for each equation. The additional terms of these equations do not kill the integrability of the typical breaking soliton equation. The Cole-Hopf transformation method and the simplified Hereman’s method are applied to conduct this analysis. 相似文献
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多线性分离变量法已成功地应用于诸多(2+1)维非线性可积系统.将该方法拓展运用于(3+1)维破碎孤子方程中,获得了含任意函数的变量分离解.通过适当地设定任意函数的形式,得到了(3+1)维破碎孤子方程丰富的局域激发模式. 相似文献
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In this article, a new (2 + 1)-dimensional local fractional breaking soliton equation is derived with the local fractional derivative. Applying the traveling wave transform of the non-differentiable type, the (2 + 1)-dimensional local fractional breaking soliton equation is converted into a nonlinear local fractional ordinary differential equation. By defining a set of elementary functions on Cantor sets, a novel analytical technique namely the Mittag–Leffler function-based method is employed for the first time ever to construct the exact solutions. The solutions on the Cantor sets are presented via the 3-D contours. It reveals that the proposed method is effective and powerful and is expected to give some inspiration for the study of the local fractional PDEs. 相似文献
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The category of foliations is considered. In this category morphisms are differentiable maps sending leaves of one foliation into leaves of the other foliation. We prove that the automorphism group of a foliation with transverse linear connection is an infinite-dimensional Lie group modeled on LF-spaces. This result extends the corresponding result of Macias-Virgós and Sanmartín Carbón for Riemannian foliations. In particular, our result is valid for Lorentzian and pseudo-Riemannian foliations. 相似文献
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借助符号计算软件,利用简化的Weiss-Tabor-Carnevale(WTC)方法,对广义的(2+1)维破碎孤子方程进行了Painleve检验,并得到了该方程的可积条件.基于多维Bell多项式的相关理论知识,导出了该方程的Hirota双线性形式,并构造出了方程的多孤子解. 相似文献
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Astha Chauhan Kajal Sharma Rajan Arora 《Mathematical Methods in the Applied Sciences》2020,43(15):8823-8840
In this work, Lie group theoretic method is used to carry out the similarity reduction and solitary wave solutions of (2 + 1)-dimensional Date–Jimbo–Kashiwara–Miwa (DJKM) equation. The equation describes the propagation of nonlinear dispersive waves in inhomogeneous media. Under the invariance property of Lie groups, the infinitesimal generators for the governing equation have been obtained. Thereafter, commutator table, adjoint table, invariant functions, and one-dimensional optimal system of subalgebras are derived by using Lie point symmetries. The symmetry reductions and some group invariant solutions of the DJKM equation are obtained based on some subalgebras. The obtained solutions are new and more general than the rest while known results reported in the literature. In order to show the physical affirmation of the results, the obtained solutions are supplemented through numerical simulation. Thus, the solitary wave, doubly soliton, multi soliton, and dark soliton profiles of the solutions are traced to make this research physically meaningful. 相似文献
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We apply the group foliation method to find noninvariant solutions of the complex Monge–Ampère equation (CMA2). We use the infinite symmetry subgroup of the CMA2 to foliate the solution space into orbits of solutions with respect to this group and correspondingly split the CMA2 into an automorphic system and a resolvent system. We propose a new approach to group foliation based on the commutator algebra of operators of invariant differentiation. This algebra together with Jacobi identities provides the commutator representation of the resolvent system. For solving the resolvent system, we propose symmetry reduction, which allows deriving reduced resolving equations. 相似文献
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《Communications in Nonlinear Science & Numerical Simulation》2011,16(3):1207-1215
This paper studies the modified Korteweg–de Vries equation with time variable coefficients of the damping and dispersion using Lie symmetry methods. We carry out Lie group classification with respect to the time-dependent coefficients. Lie point symmetries admitted by the mKdV equation for various forms for the time variable coefficients are obtained. The optimal system of one-dimensional subalgebras of the Lie symmetry algebras are determined. These are then used to determine exact group-invariant solutions, including soliton solutions, and symmetry reductions for some special forms of the equations. 相似文献