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

Masahito Hayashi, Kazuyasu Shigemoto, Takuya Tsukioka

Published 2018-05-24Version 1

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