How many types of soliton solutions do we know?

We consider several ways of how one could classify the various types of soliton solutions related to nonlinear evolution equations which are solvable by the inverse scattering method. In doing so we make use of the fundamental analytic solutions, the dressing procedure, the reduction technique and other tools characteristic for that method.

💡 Research Summary

The manuscript “How many types of soliton solutions do we know?” addresses the systematic classification of soliton solutions associated with nonlinear evolution equations (NLEEs) that are integrable via the inverse scattering method (ISM). The authors focus on Lax pairs of the Zakharov‑Shabat (ZS) type, (L(\lambda)=i\partial_x+q(x)-\lambda J), where (J) is a real diagonal Cartan element of (\mathfrak{sl}(n)) and (q(x)=