I live in the US and I have been married twice but unfortunately both marriages were not successful. In the first marriage there was very good understanding between me and my wife but due to some unfortunate events, we got separated. Eventually, I decided to marry again. I never pronounced divorce to my first wife. Since our marriage took place in my country, I went there and got a divorce certificate from the registrar. I went back to my county so that I could find another spouse. Anyway, I got engaged and applied for her visa to the US. When she got the visa I visited my country again and had the Nikaah ceremony after which I brought her to the US. Immediately after getting married I noticed that the girl is suffering from severe schizophrenia (a mental disorder). I was told that she was divorced once since her husband was greedy. When I investigated and found out that her first marriage was over within a couple of weeks due to her mental problem not because of her husband being greedy. Her parents fraudulently got her married twice and concealed her mental problems. I realized that this marriage will not work at all. Therefore divorced her officially.
Now, looking back at all the events I realize that I made a mistake by not putting more effort to resolve the issues of the first marriage. I am also aware that my first ex-wife is also repenting the situation. Now my question is whether I can get married to her again or not. There are two possibilities. In case my first marriage was not over religiously, then I believe I should be able to get back with her without remarrying her as if the marriage was never over. However, in case the marriage was over then I can not marry her unless she marries someone else and for some reason the marriage gets dissolved. Since I never pronounced divorce to her, neither sent her any documents (divorce deed etc.) what is your opinion about the dissolution of the first marriage. And in case the marriage was dissolved is there anyway of religiously marrying her again.

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.

We do not really know what you mean by 'taking divorce papers'. If you mean that you did not write the word divorce at all, or that you wrote it without having the intention of divorcing her, then your wife is not divorced and she is still considered as your wife. So, it is permissible for you to have sexual intercourse with her.

However, if you wrote the word divorce with the intention of divorce, then she is divorced. If this is the first divorce or the second divorce, it is permissible for you to take her back without a new contract or a new dowry as long as she is in her waiting period. But it is desirable to have witnesses when you take her back. However, if her waiting period has expired, it is not permissible for you to take her back except with a new marriage contract and a new dowry. Nonetheless, if this is the third divorce, then you cannot marry her again unless she marries another man a sincere marriage and he really consummates the marriage with her, and then either he divorces her or dies. For more details on this, please refer to Fatwa: 90056.

Finally, it should be noted that marital problems should be solved with wisdom and without rushing things or resorting to divorce as one always regrets it later.  

Allaah Knows best.