Topic
Elliptic coordinate system
About: Elliptic coordinate system is a research topic. Over the lifetime, 670 publications have been published within this topic receiving 11135 citations. The topic is also known as: elliptical coordinate system & elliptic coordinates.
Papers published on a yearly basis
Papers
More filters
TL;DR: In this article, a generalized Zakharov-Shabat Bargmann (g-ZS) equation is introduced by using a loop algebra G ∼, which is an isospectral problem, and is proved Liouville integrable by introducing elliptic coordinates and evolution equations.
Abstract: In this paper, a generalized Zakharov–Shabat equation (g-ZS equation), which is an isospectral problem, is introduced by using a loop algebra G ∼ . From the stationary zero curvature equation we define the Lenard gradients {gj} and the corresponding generalized AKNS (g-AKNS) vector fields {Xj} and Xk flows. Employing the nonlinearization method, we obtain the generalized Zhakharov–Shabat Bargmann (g-ZS-B) system and prove that it is Liouville integrable by introducing elliptic coordinates and evolution equations. The explicit relations of the Xk flows and the polynomial integrals {Hk} are established. Finally, we obtain the finite-band solutions of the g-ZS equation via the Abel–Jacobian coordinates. In addition, a soliton hierarchy and its Hamiltonian structure with an arbitrary parameter k are derived.
10 citations
TL;DR: In this paper, it was shown that the phenomenon of R-separation occurs nontrivially for the Helmholtz equation on a pseudo-Riemannian manifold, and that a satisfactory theory of variable separation for the H-means must incorporate R -separation.
Abstract: We present examples to show that the phenomenon ofR-separation occurs nontrivially for the Helmholtz equation on a pseudo-Riemannian manifold.R-separable coordinate systems can be both orthogonal and non-orthogonal and a given coordinate system mayR-separate in more than one way. A satisfactory theory of variable separation for the Helmholtz equation must incorporateR-separation.
10 citations
TL;DR: The general-purpose partial differential equation (PDE) solver PDE2D uses a Galerkin finite element method, with standard triangular elements of up to fourth degree, to solve PDEs in general 2D regions, and once the global coordinate system is defined, the rest of the input is as simple as if the region were a rectangle.
10 citations
TL;DR: In this article, the authors proposed a conformal transformation that maps an infinite chevron in the complex Jacobi coordinate z=x+iy plane to an infinite strip in the w=u+iv plane, where u is the reaction coordinate; v is the vibrational coordinate.
Abstract: In order to build wavefunctions for colinear reactive scattering from solutions of a one‐dimensional Schrodinger equation, it is necessary to change the coordinate system from mass‐weighted Jacobi coordinates (x,y) to a system of reaction coordinates that retains the ∇2 character of the kinetic energy operator. Connor and Marcus [J. Chem. Phys. 53, 3188 (1970)] proposed a conformal transformation that maps an infinite chevron in the complex Jacobi coordinate z=x+iy plane to an infinite strip in the w=u+iv plane. u is the reaction coordinate; v is the (generalized) vibrational coordinate. We show that computational difficulties associated with this transformation can be partially removed by either of two methods of mapping part of the w‐plane strip into an infinte strip in a third plane, t=r+is. The first method introduces ’’dipole pairs’’ in the w plane. The second introduces a slit in the w‐plane strip. Relative advantages of the two methods are discussed. A Connor–Marcus‐like map from a semi‐infinite tr...
10 citations
TL;DR: In this paper, a method for the interpolation of a potential from data for the C 2v and C ∞v configurations for atom-diatomic systems is presented in terms of elliptical coordinates.
10 citations