标题： 可积的短脉冲方程离散化 显示英文标题

标题： Integrable discretizations of the short pulse equation

摘要： 在本文中，我们提出了短脉冲（SP）方程的可积半离散和全离散模拟。 构造的关键是SP方程的双线性形式和解的行列式结构。 我们还给出了SP方程半离散和全离散模拟的N孤子解的行列式公式，从中可以生成多环状和多呼吸子解。 在连续极限下，全离散SP方程收敛到半离散SP方程，然后收敛到连续SP方程。 基于半离散SP方程，提出了一种可积的数值方案，即自适应移动网格方案，并用于短脉冲方程的数值计算。 显示英文摘要

摘要： In the present paper, we propose integrable semi-discrete and full-discrete analogues of the short pulse (SP) equation. The key of the construction is the bilinear forms and determinant structure of solutions of the SP equation. We also give the determinant formulas of N-soliton solutions of the semi-discrete and full-discrete analogues of the SP equations, from which the multi-loop and multi-breather solutions can be generated. In the continuous limit, the full-discrete SP equation converges to the semi-discrete SP equation, then to the continuous SP equation. Based on the semi-discrete SP equation, an integrable numerical scheme, i.e., a self-adaptive moving mesh scheme, is proposed and used for the numerical computation of the short pulse equation.