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331.
分别讨论了以第二类Chebyshev多项式的零点、Jacobi多项式的零点、第一类Chebyshev多项式的零点为插值结点组的五类Kantorovich型插值算子在Orlicz空间内的逼近问题,得到了逼近阶的上界估计. 相似文献
332.
In this article, we propose an alternative approach of the generalized and improved (G'/G)-expansion method and build some new exact traveling wave solutions of three nonlinear evolution equations, namely the Boiti- Leon-Pempinelle equation, the Pochhammer-Chree equations and the Painleve integrable Burgers equation with free parameters. When the free parameters receive particular values, solitary wave solutions are constructed from the traveling waves. We use the Jacob/elliptic equation as an auxiliary equation in place of the second order linear equation. It is established that the proposed algorithm offers a further influential mathematical tool for constructing exact solutions of nonlinear evolution equations. 相似文献
333.
Pulse dynamics and stability in optical fibers in the presence of both self-steepening and quintic nonlinear effects are analyzed. Propagating profiles of the quintic derivative nonlinear Schrodinger model are isolated via two invariants of motion. The resulting canonical equation admits exact periodic propagating patterns in terms of the Jacobi elliptic functions, and solitary pulses are recovered in the long wave limit, i.e. degenerate cases of periodic profiles where each pulse is widely separated from the adjacent ones. Two families of such exact wave profiles are identified. The first one has a precise constraint concerning the magnitude of self-steepening and quintic nonlinear effects, while the second one permits more freedom. The reduction to the well established temporal soliton in an optical fiber waveguide in the absence of self-steepening and quintic nonlinearity is demonstrated explicitly. Numerical simulations are performed to identify regimes of parameter values where robust propagation patterns exist. 相似文献
334.
Abundant new exact solutions of the Schamel-Korteweg-de Vries (S-KdV) equation and modified Zakharov- Kuznetsov equation arising in plasma and dust plasma are presented by using the extended mapping method and the availability of symbolic computation. These solutions include the Jacobi elliptic function solutions, hyperbolic function solutions, rational solutions, and periodic wave solutions. In the limiting cases, the solitary wave solutions are obtained and some known solutions are also recovered. 相似文献
335.
In this paper, we will use a simple and direct method to obtain some particular solutions of (2+1)- dimensional and (3+ 1)-dimensional KP equation expressed in terms of the Kleinian hyperelliptic functions for a given curve y^2 = f(x) whose genus is three. We observe that this method generalizes the auxiliary method, and can obtain the hyperelliptic functions solutions. 相似文献
336.
AN INVERSE EIGENVALUE PROBLEM FOR JACOBI MATRICES 总被引:7,自引:0,他引:7
Er-xiong Jiang 《计算数学(英文版)》2003,21(5):569-584
Let T1,n be an n x n unreduced symmetric tridiagonal matrix with eigenvaluesand is an (n - 1) x (n - 1) submatrix by deleting the kth row and kth column, k = 1, 2,be the eigenvalues of T1,k andbe the eigenvalues of Tk+1,nA new inverse eigenvalues problem has put forward as follows: How do we construct anunreduced symmetric tridiagonal matrix T1,n, if we only know the spectral data: theeigenvalues of T1,n, the eigenvalues of Ti,k-1 and the eigenvalues of Tk+1,n?Namely if we only know the data: A1, A2, An,how do we find the matrix T1,n? A necessary and sufficient condition and an algorithm ofsolving such problem, are given in this paper. 相似文献
337.
Li-lianWang Ben-yuGuo 《计算数学(英文版)》2003,21(3):325-338
Jacobi polynomial approximations in multiple dimensions are investigated.They are applied to numerical solutions of singular differential equations.The convergence analysis and numerical results show their advantages. 相似文献
338.
YANGYong YANZhen-Ya 《理论物理通讯》2002,38(6):657-659
In this letter the three-dimensional nonlinear Helmholtz equation is investigated.which describes electromagnetic wave propagation in a nonlinear Kerr-type medium such that sixteen families of new Jacobi elliptic function solutions are obtained,by using our extended Jacobian elliptic function expansion method.When the modulus m-→1 or 0,the corresponding solitary waves including bright solitons,dark solitons and new line solitons and singly periodic solutions can be also found. 相似文献
339.
DOU Fu-Quan SUN Jian-An DUAN Wen-Shan LU Ke-Pu 《理论物理通讯》2007,48(4):584-590
Based on the multi-linear variable separation approach, a class of exact, doubly periodic wave solutions for the (3+1)-dimensional Jimbo-Miwa equation is analytically obtained by choosing the Jacobi elliptic functions and their combinations. Limit cases are considered and some new solitary structures (new dromions) are derived. The interaction properties of periodic waves are numerically studied and found to be inelastic. Under long wave limit, two sets of new solution structures (dromions) are given. The interaction properties of these solutions reveal that some of them are completely elastic and some are inelastic. 相似文献
340.
ZHENG Ying ZHANG Yuan-Yuan ZHANG Hong-Qing 《理论物理通讯》2006,46(1):5-9
In this paper, an extended Jacobi elliptic function rational expansion method is proposed for constructing new forms of exact Jacobi elliptic function solutions to nonlinear partial differential equations by means of making a more general transformation. For illustration, we apply the method to the (2+1)-dimensional dispersive long wave equation and successfully obtain many new doubly periodic solutions, which degenerate as soliton solutions when the modulus m approximates 1. The method can also be applied to other nonlinear partial differential equations. 相似文献