The emergence of solitons of the korteweg‐de vries equation from arbitrary initial conditions

摘要

AbstractWe study the solutionu(x, t) of the Korteweg‐de Vries equationut− 6uux+uxxx= 0 with arbitrary initial conditionsu(x, 0) =u0(x),u0(x) decaying sufficiently rapidly as ξ→∞. Using the method of the inverse scattering transformation we analyse the Gel'fand‐Levitan equation in all coordinate systems moving to the right and give a complete and rigorous description of the emergence o