Good book on solitons focusing mainly on analysis of PDE

Question

I have a good background in PDEs and functional analysis and I would like to learn more about solitons. The most popular references that I see pop up are Drazin and Kasman, but the first is a little less rigorous than I prefer and the second focuses on algebra, which is just not to my taste. Does anyone have a good reference for solitons from an analysis point of view? Thanks in advance!

Answer 1

Indeed, many books on solitary waves are written from a physical perspective. From a mathematical physics or applied mathematics point of view, I would suggest these:

A.C. Newell: Solitons in Mathematics and Physics. SIAM, 1985. books.google doi:10.1137/1.9781611970227

A.-M. Wazwaz: Partial Differential Equations and Solitary Waves Theory. Springer, 2009. books.google doi:10.1007/978-3-642-00251-9

Answer 2

A couple of books I found helpful were

Solitons and the Inverse Scattering Transform, by Ablowitz and Segur.

Slightly more focused on solitons in optical fibers:

Mathematical Principles of Optical Fiber Communications, by J. K. Shaw.