We give a complete characterization of the reflectionless Schrödinger operators on the line with integrable potentials, solve the inverse scattering problem of reconstructing such potentials from the eigenvalues and norming constants, and derive the corresponding generalized soliton solutions of the Korteweg–de Vries equation.

中文翻译：

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具有KdV方程的可积势和广义孤子解的无反射Schrödinger算子的逆散射

我们对具有可积势的线上的无反射Schrödinger算子进行了完整的刻画，解决了根据特征值和范数常数重建此类势的逆散射问题，并推导了Korteweg-de Vries方程的相应广义孤子解。