Without divorce second marriage is an offence under Indian laws. So the second marriage is null and void under Indian law.In such a case Live in relationship also will be treated as an act of adultery .Section 17 HMA says that any marriage between Hindus is void if on the date of such marriage, either party had a husband or wife living.
So better you file a divorce case immediately in Indian court . After getting the decree of divorce legally marry the second wife. If your wife not appear before the court after serving summons to her you can get exparty divorce from the court it will take only 2 or 3 months. All other proceedings will take much time. Or other wise file a Divorce by Mutual Consent .The Conditions required under section 13B of the Hindu Marriage Act are as follows:
(i) Husband and wife have been living separately for a period of one year or more,
(ii) That they are unable to live together,
(iii) And that both husband and wife have mutually agreed that the marriage has totally collapsed, hence marriage should be dissolved.
As per latest supreme court rulings Six-month cooling period for granting divorce is waived and you got early divorce decree