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Exact solutions of KdV equation with time-dependent coefficients   总被引:1,自引:0,他引:1  
In this paper, we study the Korteweg-de Vries (KdV) equation having time dependent coefficients from the Lie symmetry point of view. We obtain Lie point symmetries admitted by the equation for various forms for the time-dependent coefficients. We use the symmetries to construct the group-invariant solutions for each of the cases of the arbitrary coefficients. Subsequently, the 1-soliton solution is obtained by the aid of solitary wave ansatz method. It is observed that the soliton solution will exist provided that these time-dependent coefficients are all Riemann integrable.  相似文献
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Soliton solutions of Burgers equations and perturbed Burgers equation   总被引:1,自引:0,他引:1  
This paper carries out the integration of Burgers equation by the aid of tanh method. This leads to the complex solutions for the Burgers equation, KdV-Burgers equation, coupled Burgers equation and the generalized time-delayed Burgers equation. Finally, the perturbed Burgers equation in (1+1) dimensions is integrated by the ansatz method.  相似文献
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This paper develops algorithms for solving an undetermined coefficient problem for a wave equation. The algorithms are based on an integral representation for the solution to the wave equation obtained by using transmutation. The convergence of the algorithm is studied and numerical experiments are performed.  相似文献
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Invariant factors of bivariate orthogonal polynomials inherit most of the properties of univariate orthogonal polynomials and play an important role in the research of Stieltjes type theorems and location of common zeros of bivariate orthogonal polynomials. The aim of this paper is to extend our study of invariant factors from two variables to several variables. We obtain a multivariate Stieltjes type theorem, and the relationships among invariant factors, multivariate orthogonal polynomials and the corresponding Jacobi matrix. We also study the location of common zeros of multivariate orthogonal polynomials and provide some examples of tri-variate.  相似文献
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The probability distribution of the number of players in the last round of a matching problem is analyzed and the existence of the limiting distribution is proved by using convolution method.  相似文献
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Problem solving and justification of a diversified group of two-year college students was compared with approaches of younger elementary and secondary school students working on the same tasks. The students in this study were engaged in thoughtful mathematics. Both groups found patterns, justified that their patterns were reasonable and, utilized similar strategies for their solutions and methods of justification. They were also able to make connections and build isomorphisms among the various problems.  相似文献
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In this paper, we consider the problem of constructing partitions of the points of a Hermitian unital into pairwise disjoint blocks, commonly known as spreads. We generalize a construction of Baker et al. (In Finite Geometry and Combinatorics, Vol. 191 of London Math. Soc. Lecture Not Ser., pages 17–30. Cambridge University Press, Cambridge, 1993.) to provide a new infinite family of spreads. Morover, we develop a structural connection between these new spreads of the Hermitian unital in PG(2, q2) and the subregular spreads of PG(3, q), allowing us to christen a new “subregular” family of spreads in the Hermitian unital in PG(2, q2).  相似文献
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