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Higher Order Transformation
Recursion Operator and Lax Pair
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Ablowitz arbitrary function Asano asymptotic B+(x boundary values Cauchy coefficients condition conservation law consider constant construct convergence coordinates defined denotes derivatives differential equations equivalent Euler-Lagrange equation evolution equation Example exists f+(x finite Fredholm determinant Fredholm theory given hence identity independent integral equation integral kernel integral operator introduce invariant manifold invariant solution inverse scattering inverse-scattering method Jost solution KdV equation Lax pair Lemma Let Q Lie algebra linear Manakov mapping Marchenko equation nonlinear equations Note obtain off-diagonal parameter point transformation Poisson bracket potential Q Proof properties Q e CF(0 recursion operator regular relation respect satisfies scattering data scattering problem soliton space spectral problem symmetry vanishes variables vector field yields zero ZS-AKNS system