I'm now studying inverse scattering method for KDV equation. Namely, Through $$\psi_{xx}-(u-\lambda)\psi=0,u(x,0)=f(x)$$ we can solve the KDV equation $u_t-6uu_x+u_{xxx}=0$,when $x\to|\infty|,u\to0,u_x\to0$.
The essay "The Korteweg-de Vries Equation:A survey of Results" written by Robert M.Miura says that all discrete eigenvalues $\lambda<0$,while the continuous eigenvalue $\lambda>0$, I don't know why. I need a help.
