2001/11/30 by Avinash Khare, Uday Sukhatme, U. Sukhatme
Mathematics · Physics and Astronomy · #Elliptic function #Jacobi elliptic functions #Korteweg–de Vries equation #Lambda #Mathematical analysis #Mathematical physics #Mathematics #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Nonlinear system #Physics #Quantum Mechanics and Non-Hermitian Physics #Quantum mechanics #Superposition principle #cond-mat #hep-th #math-ph #math.AP #math.MP #nlin.SI #quant-ph
paper · pdf · doi:10.1103/physrevlett.88.244101
published as Phys.Rev.Lett. 88 (2002) 244101 · 7 pages, 1 figure
arxiv created 2001/11/30 · openalex publication_date 2002/05/30 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Several nonlinear systems such as the Korteweg-de Vries (KdV) and modified KdV equations and lambda phi(4) theory possess periodic traveling wave solutions involving Jacobi elliptic functions. We show that suitable linear combinations of these known periodic solutions yield many additional solutions with different periods and velocities. This linear superposition procedure works by virtue of some remarkable new identities involving elliptic functions.