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排序方式: 共有379条查询结果,搜索用时 31 毫秒
1.
We consider the Hankel determinant generated by the Gaussian weight with two jump discontinuities. Utilizing the results of Min and Chen [Math. Methods Appl Sci. 2019;42:301‐321] where a second‐order partial differential equation (PDE) was deduced for the log derivative of the Hankel determinant by using the ladder operators adapted to orthogonal polynomials, we derive the coupled Painlevé IV system which was established in Wu and Xu [arXiv: 2002.11240v2] by a study of the Riemann‐Hilbert problem for orthogonal polynomials. Under double scaling, we show that, as , the log derivative of the Hankel determinant in the scaled variables tends to the Hamiltonian of a coupled Painlevé II system and it satisfies a second‐order PDE. In addition, we obtain the asymptotics for the recurrence coefficients of orthogonal polynomials, which are connected with the solutions of the coupled Painlevé II system. 相似文献
2.
Pavel Trojovský 《Journal of Difference Equations and Applications》2017,23(10):1737-1746
This paper is devoted to a generalization of some previous results, as we completely solve a linear homogeneous difference equation of the second order with an exponential coefficient. 相似文献
3.
借助双Casoratian技巧和构造双Wronski行列式元素的矩阵方法,求出2个位势的Ablowitz-Ladik等谱方程的Complexiton解和周期解,并通过将矩阵取成不同的组合类型,进而分别得到该方程具有双Casorati行列式形式的新解,即Complexiton解与类有理解的混合解、Complexiton解与Matveev解的混合解. 相似文献
4.
5.
针对线性代数教材中一道行列式证明题,利用行列式的性质,给出多种证明方法,旨在启发学生对相关行列式计算或证明题的解题方法进行探索. 相似文献
6.
设R为非负交换整半环,用M_n(R)表示R上所有n×n矩阵构成的矩阵半环.令T是M_n(R)到其自身的线性变换,若T满足|T(X)|~+=|X|~+,■X∈M_n(R)(或|T(X)|~-=|X|~-,(?)X∈Mn(R)),称T为M_n(R)上保持正行列式(负行列式)的线性变换.刻画了n≥4时,M_n(R)上保持正行列式/负行列式的线性满射形式. 相似文献
7.
从Vandermonde行列式出发,给出了Cayley-Hamilton定理的一个新的证明,也给出了有限维向量空间的一些结论的新的证明. 相似文献
8.
The modified discrete KP equation is the Bäcklund transformation for the Hirota’s discrete KP equation or the Hirota-Miwa equation. We construct the modified discrete KP equation with self-consistent sources via source generation procedure and clarify the algebraic structure of the resulting coupled modified discrete KP system by presenting its discrete Gram-type determinant solutions. It is also shown that the commutativity between the source generation procedure and Bäcklund transformation is valid for the discrete KP equation. Finally, we demonstrate that the modified discrete KP equation with self-consistent sources yields the modified differential-difference KP equation with self-consistent sources through a continuum limit. The continuum limit of an explicit solution to the modified discrete KP equation with self-consistent sources also gives the explicit solution for the modified differential-difference KP equation with self-consistent sources. 相似文献
9.
10.
Guo-Dong LinYi-Tian Gao Zhi-Yuan SunXin Yu De-Xin Meng 《Applied mathematics and computation》2011,217(9):4805-4811
Under investigation in this paper is a variable-coefficient variant Boussinesq (vcvB) model for the nonlinear and dispersive long gravity waves in shallow water traveling in two horizontal directions with varying depth. Connection between the vcvB model and a variable-coefficient Ablowitz-Kaup-Newell-Segur system is revealed under certain constraints with the help of the symbolic computation. Multi-solitonic solutions in terms of the double Wronskian determinant for the vcvB model are derived. Interactions among the vcvB-solitons are discussed. A novel dynamic property is observed, i.e., the coexistence of elastic-inelastic-interactions. 相似文献