Interaction of Two Pulsatory Waves of the Korteweg-de Vries Equation in a Zigzag Hyperbolic Structure

• 作者: Victor A. Miroshnikov
• 来源期刊: 美国计算数学期刊(英文)
• 学科: 数学
• 关键词: KDV Equation TWO Pulsatory WAVES ZHT Structure Experimental Theoretical COMPUTATION
• 年，卷（期）: 2014,（3）
• 页码范围: 254-270
• 页数: 17页
• 分类号: O1

摘要

A new exact solution for nonlinear interaction of two pulsatory waves of the Korteweg-de Vries (KdV) equation is computed by decomposition in an invariant zigzag hyperbolic tangent (ZHT) structure. A computational algorithm is developed by experimental programming with lists of equations and expressions. The structural solution is proved by theoretical programming with symbolic general terms. Convergence, tolerance, and summation of the ZHT structural approximation are discussed. When a reference level vanishes, the two-wave solution is reduced to the two-soliton solution of the KdV equation.