Section 31. A married woman residing without this commonwealth, and owning in her own right real estate situated herein, whose husband abandoning and not sufficiently maintaining her has absented himself from the place where they last dwelt together, may petition the probate court in any county where the land lies, describing such real estate and praying for authority to sell and convey it in the same manner and with the same effect as if she were sole. The court, after such notice as it may order, if it finds that the petitioner has been abandoned by her husband and that he does not sufficiently maintain her, may authorize the petitioner to sell and convey within one year from the date of such decree such real estate as if she were sole.