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We study the nonlocal modified Korteweg-de Vries (mKdV) equations obtainedfrom AKNS scheme by Ablowitz-Musslimani type nonlocal reductions. We first findsoliton solutions of the coupled mKdV system by using the Hirota direct method.Then by using the Ablowitz-Musslimani reduction formulas, we find one-, two-,and three-soliton solutions of local and nonlocal complex mKdV and mKdVequations. The soliton solutions of these equations are of two types. We giveone-soliton solutions of both types and present only first type of two- andthree-soliton solutions. We illustrate our soliton solutions by plotting theirgraphs for particular values of the parameters.

Nonlocal Modified KdV Equations and Their Soliton Solutions