Abstract
Certain partial differential equations have localized stable traveling-wave solutions. If the underlying system is integrable, there are infinitely many conserved quantities and this in turn implies that these traveling waves—solitons—in fact scatter elastically. The chapter focuses on the scattering properties of solitons. Integrability is a very strong property and has many important consequences, including the possibility of solving the initial value problem using the inverse scattering transform method. It is, however, possible to study soliton scattering even if the system is not completely integrable. There are many other soliton equations with two-soliton solution (2SS) of different structure, but still have very much the same behavior under scattering. Some coupled soliton equations have two different kinds of soliton solutions. One of such equations—Hirota–Satsuma equation—is presented.
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