Soliton solutions of an integrable nonlocal modified Korteweg-de Vries equation through inverse scattering transform

摘要

It is well known that the nonlinear Schr\"odinger (NLS) equation is a veryimportant integrable equation. Ablowitz and Musslimani introduced andinvestigated an integrable nonlocal NLS equation through inverse scatteringtransform. Very recently, we proposed an integrable nonlocal modifiedKorteweg-de Vries equation (mKdV) which can also be found in a paper ofAblowitz and Musslimani. We have constructed the Darboux transformation andsoliton solutions for the nonlocal mKdV equation. In this paper, we willinvestigate further the nonlocal mKdV equation. We will give its exactsolutions including soliton and breather through inverse scatteringtransformation. These solutions have some new properties, which are differentfrom the ones of the mKdV equation.