Solitons on a Periodic Wave Background of the Modified KdV-Sine-Gordon Equation

摘要

The B(a)cklund transformation(BT) of the mKdV-sG equation is constructed by introducing a new transformation.Infinitely many nonlocai symmetries are obtained in terms of its BT.The soliton-periodic wave interaction solutions are explicitly derived by the classical Lie-group reduction method.Particularly,some special concrete soliton and periodic wave interaction solutions and their behaviours are discussed both in analytical and graphical ways.