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KdV Schrodinger spectral problem ( $- ϕ_{xx} + u ϕ = λ ϕ$ )

The inverse-scattering spectral problem associated with this KdV convention is

- ϕ_{xx} + u (x, t) ϕ = λ (t) ϕ .

For

Q = ϕ_{t} + u_{x} ϕ - 2 (u + 2 λ) ϕ_{x},

differentiation gives the Wronskian identity

\partial_{x} (ϕ_{x} Q - ϕ Q_{x}) = ϕ^{2} [\dot{λ} - (u_{t} + u_{xxx} - 6 u u_{x})] .

Table of contents 66 2
- Isospectrality of the KdV discrete spectrum KdV Schrodinger spectral problem 46 1
  - Evolution of a KdV discrete norming constant Isospectrality of the KdV discrete spectrum 16

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