The Construction of the mKdV Cyclic Symmetric $N$-soliton Solution by the Bäcklund Transformation

Abstract

We study group theoretical structures of the mKdV equation. The Schwarzian type mKdV equation has the global Möbius group symmetry. The Miura transformation makes a connection between the mKdV equation and the KdV equation. We find the special local Möbius transformation on the mKdV one-soliton solution which can be regarded as the commutative KdV Bäcklund transformation can generate the mKdV cyclic symmetric $N$-soliton solution. In this algebraic construction to obtain multi-soliton solutions, we could observe the addition formula.

14 pages

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