Generalized Heisenberg Ferromagnet type Equation and Modified Camassa-Holm Equation: Geometric Formulation, Soliton Solutions and Equivalence

2020/02/21 by Umurzakhova, Zhanar, Myrzakul, Tolkynay, Yesmakhanova, Kuralay +3
#Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences

paper · doi:10.48550/arxiv.2002.10969

Abstract

We study the integrability and equivalence of a generalized Heisenberg ferromagnet-type equation (GHFE). The different forms of this equation as well as its reduction are presented. The Lax representation (LR) of the equation is obtained. We observe that the geometrical and gauge equivalent counterpart of the GHFE is the modified Camassa-Holm equation (mCHE) with an arbitrary parameter κ. Finally, the 1-soliton solution of the GHFE is obtained.

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