Integrable discretization and its applications

Discretization of Surfaces and Integrable Systems

Nonuniform Discretization for Kinodynamic Motion Planning and its Applications

The first main result of this paper is a novel nonuniform discretization approximation method for the kinodynamic motion-planning problem. The kinodynamic motion-planning problem is to compute a collision-free, time-optimal trajectory for a robot whose accelerations and velocities are bounded. Previous approximation methods are all based on a uniform discretization in the time space. On the con...

An integrable semi-discretization of the Camassa-Holm equation and its determinant solution

Abstract. An integrable semi-discretization of the Camassa-Holm equation is presented. The keys of its construction are bilinear forms and determinant structure of solutions of the CH equation. Determinant formulas of N-soliton solutions of the continuous and semi-discrete Camassa-Holm equations are presented. Based on determinant formulas, we can generate multi-soliton, multi-cuspon and multi-...

Integrable semi-discretization of the coupled nonlinear Schrödinger equations

A system of semi-discrete coupled nonlinear Schrödinger equations is studied. To show the complete integrability of the model with multiple components, we extend the discrete version of the inverse scattering method for the single-component discrete nonlinear Schrödinger equation proposed by Ablowitz and Ladik. By means of the extension, the initial-value problem of the model is solved. Further...

Benford Distribution and its Applications

‎This papers considers the Benford distribution as one the interesting rules of probability theory‎. ‎This rule shows that‎, ‎despite of usual underestanding about the uniform distribution of digites‎ ‎for lieing on different positions in numbers‎, ‎digits are distributed according to an non uniform distributions for numbers araising from many natural phonemena‎. ‎Benford distribution proposes ...