Huygens' Principle in Minkowski Spaces and Soliton Solutions of the Korteweg-de Vries Equation

1997/04/18 by Yuri Berest, Y. Berest, I. Loutsenko +1 · 2 citations
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Mathematical Analysis and Transform Methods #Nonlinear Waves and Solitons #nlin.SI #solv-int

paper · pdf · doi:10.1007/s002200050235

23 pages, LaTeX, to be published in Comm.Math.Phys (1997)

arxiv created 1997/04/18 · openalex publication_date 1997/12/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A new class of linear second order hyperbolic partial differential operators satisfying Huygens' principle in Minkowski spaces is presented. The construction reveals a direct connection between Huygens' principle and the theory of solitary wave solutions of the Korteweg-de Vries equation.

Citations

• Huygens’ principle and hadamard’s conjecture
• Hadamard's problem and coxeter groups: New examples of Huygens' equations
• ASSOCIATED STURM-LIOUVILLE SYSTEMS

Cited by

• Huygens–Fresnel principle [wikipedia]
• Korteweg–De Vries equation [wikipedia]