2011/11/21 by Y. Ben-Aryeh, Ben-Aryeh, Y.
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Nonlinear Photonic Systems #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.1111.5226
openalex publication_date 2011/11/21 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
Soliton solutions of non-linear NLS and KdV equations are related to compatibility condition between matrices M and H describing the movement of an auxilary function Psi in the x,t plane with a zero curvature condition. Non-linear equation for a function u is obtained by the compatibility equation where the matrix elements of M and H include only functions of u and its derivatives. By solving the equations of motion for Psi a soliton solution for u is obtained. Explicit calculations are made with two-dimensional and one-dimensional wave functions Psi for the NLS and KdV solitons, correspondingly.