It's not so lengthy but it covers important points. Especially, it briefs LAX pair methods, which essentially tell how the scattering data evolves.
My understanding is that this topic demands good mathematics and, perhaps more improtantly, a good grasp of quantum mechanics (specifically, the specitral theory of the static schrodinger equation along the whole axis). So, not so many people come to this topic so frequently and, therefore, you may not be able to get free copies of some good books. If you are really interested in this topic, it's very well worthy to go to a library, review some of the books and buy one or two. Here is what I think, even though it's about the nonlinear PDE's, a good book should concentrate more on the time independent linear schrodinger equation.