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m →Scattering data time evolution: clarification of linear differential operators |
m →Inverse scattering transform: Corrected equation |
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The [[Gelfand–Levitan–Marchenko integral equation|Marchenko integral equation]] is a linear integral equation solved for <math display="inline">K(x,y,t)</math>.{{sfn|Aktosun|2009}}{{rp|4968-4969}}
: <math> K(x,z,t)+F(x+z,t)+ \int^{\infty}_{x} K(x,y,t)F(y+z,t) \ dy=0 </math>
The solution to the Marchenko equation, <math display="inline">K(x,y,t) </math>, generates the solution <math display="inline">u(x,t)</math> to the nonlinear partial differential equation.{{sfn|Aktosun|2009}}{{rp|4969}}
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