2008/10/20 by Carl M. Bender, Fred Cooper, Avinash Khare +2 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Function (biology) #Geometry #Korteweg–de Vries equation #Mathematical physics #Mathematics #Momentum (technical analysis) #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Nonlinear system #Physics #Quantum mechanics #Scaling #hep-th #math-ph #math.MP
paper · pdf · doi:10.1007/s12043-009-0129-1
12 pages, 5 figures
arxiv created 2008/10/20 · openalex publication_date 2009/08/01 · arxiv updated 2015/05/12 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/29
In an earlier paper Cooper, Shepard, and Sodano introduced a generalized KdV equation that can exhibit the kinds of compacton solitary waves that were first seen in equations studied by Rosenau and Hyman. This paper considers the PT-symmetric extensions of the equations examined by Cooper, Shepard, and Sodano. From the scaling properties of the PT-symmetric equations a general theorem relating the energy, momentum, and velocity of any solitary-wave solution of the generalized KdV equation is derived, and it is shown that the velocity of the solitons is determined by their amplitude, width, and momentum.