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71.
Modular and quasimodular solutions of a specific second order differential equation in the upper-half plane, which originates from a study of supersingular j-invariants in the first author's work with Don Zagier, are given explicitly. Positivity of Fourier coefficients of some of the solutions as well as a characterization of the differential equation are also discussed. 相似文献
72.
Bruzón M. S. Gandarias M. L. Muriel C. Ramírez J. Saez S. Romero F. R. 《Theoretical and Mathematical Physics》2003,137(1):1367-1377
We use the classical and nonclassical methods to obtain symmetry reductions and exact solutions of the (2+1)-dimensional integrable Calogero–Bogoyavlenskii–Schiff equation. Although this (2+1)-dimensional equation arises in a nonlocal form, it can be written as a system of differential equations and, in potential form, as a fourth-order partial differential equation. The classical and nonclassical methods yield some exact solutions of the (2+1)-dimensional equation that involve several arbitrary functions and hence exhibit a rich variety of qualitative behavior. 相似文献
73.
Mathematical Notes - 相似文献
74.
We construct classical point symmetry groups for joint pairs of evolution equations (systems of equations) of integrable hierarchies related to the auxiliary equation of the method of the inverse problem of second order. For the two cases: the hierarchy of Korteweg--de Vries (KdV) equations and of the systems of Kaup equations, we construct simultaneous solutions invariant with respect to the symmetry group. The problem of the construction of these solutions can be reduced, respectively, to the first and second Painlevé equations depending on a parameter. The Painlevé equations are supplemented by the linear evolution equations defining the deformation of the solution of the corresponding Painlevé equation. 相似文献
75.
We state a theorem on the instability of self-similar cycles and tori of a certain type in a system which is a quasinormal form of a boundary-value problem for a nonlinear wave equation in the square. 相似文献
76.
Spectral and Pseudospectral Approximations Using Hermite Functions: Application to the Dirac Equation 总被引:1,自引:0,他引:1
We consider in this paper spectral and pseudospectral approximations using Hermite functions for PDEs on the whole line. We first develop some basic approximation results associated with the projections and interpolations in the spaces spanned by Hermite functions. These results play important roles in the analysis of the related spectral and pseudospectral methods. We then consider, as an example of applications, spectral and pseudospectral approximations of the Dirac equation using Hermite functions. In particular, these schemes preserve the essential conservation property of the Dirac equation. We also present some numerical results which illustrate the effectiveness of these methods. 相似文献
77.
In this note we show that all diffeomorphisms close enough to the time-one map of the frame flow on certain negatively curved manifolds are ergodic. As a simple corollary we deduce that the frame flows are ergodic for all compact manifolds with curvature pinched sufficiently close to –1, thus providing results in the case of manifolds of dimension 7 or 8 which were missing from the results of Brin and Karcher. 相似文献
78.
Oleg Palumbíny 《Czechoslovak Mathematical Journal》2003,53(2):467-477
The paper deals with oscillation criteria of fourth order linear differential equations with quasi-derivatives. 相似文献
79.
We construct a multiplicative group structure in the class of integro-differential operators specific for a polydisk which was introduced by I. I. Bavrin. We indicate two applications of these operators to solution of functional equations. 相似文献
80.
Madalina Deaconu Nicolas Fournier Etienne Tanré 《Methodology and Computing in Applied Probability》2003,5(2):131-158
By continuing the probabilistic approach of Deaconu et al. (2001), we derive a stochastic particle approximation for the Smoluchowski coagulation equations. A convergence result for this model is obtained. Under quite stringent hypothesis we obtain a central limit theorem associated with our convergence. In spite of these restrictive technical assumptions, the rate of convergence result is interesting because it is the first obtained in this direction and seems to hold numerically under weaker hypothesis. This result answers a question closely connected to the Open Problem 16 formulated by Aldous (1999). 相似文献