Focusing mKdV Breather Solutions with Nonvanishing Boundary Conditions by the Inverse Scattering Method

TL;DR

This paper derives explicit focusing mKdV breather solutions with nonvanishing boundary conditions using the inverse scattering method, including a generalization of the Double Pole solution in the zero-frequency limit.

Contribution

It provides a new explicit formulation of focusing mKdV breather solutions with nonzero vacuum parameters using inverse scattering, and generalizes the Double Pole solution.

Findings

Explicit breather solutions with nonvanishing boundary conditions derived.

Factorization and simplification of solutions achieved.

Generalization of the Double Pole solution obtained in the zero-frequency limit.

Abstract

Using the Inverse Scattering Method with a nonvanishing boundary condition, we obtain the square k^2 of a focusing modified Korteweg-de Vries (mKdV) breather solution with non zero vacuum parameter b^2 . We are able to factorize and simplify it in order to get explicitly the associated mKdV breather solution k with non zero vacuum parameter b. Moreover, taking the limiting case of zero frequency, we obtain a generalization of the Double Pole solution introduced by M.Wadati et al.