What is Shoivavim?What is Shovavim Tat? what is its significance and how is it for lack of a better term celebrated?
Sources Shaar HaKavanot Drushei HaLaila
Sha'ar Ruah Hakodesh Tikun 27 page 17c
There is an ancient minhag in all of Israel to fast forty days consecutively that are from the first day of Parashat Shemot until Parashat Teruma and a bit of Tetzaveh. They are given the siman שובו בנים return children Shovvavim which are the Roshei Teivot Shemot V'aera, Bo, Beshalah, Yitro, Mishpatim.Beshalah, Yitro, Mishpatim.
From Devarim Shebikedusha Chapter 4 in Hok L'Yisrael- in fact the musar section of Hok L'Yisrael for the entire six weeks typically deal with the Shovvavim):
The time of year when the Torah portions of Shemot through Mishpatim are read are believed to hold great power of repentanc3 and during this period the multitudes approach G-d to repent of the sin of their youth by which they have blemished the sign of the holy covenant.
There is also the Sefer Beniyahu BenYehoida which deals with the primary tikkunim of this period of time. There are varying minhagim of the Mekubalim during this time. Many Mekubalim fast day and night Shavua L'Shavua, while others will fast 2-3 days(day and night) each week, based on the Arizal's teaching that 2 days(day and night) are equal to 27days of fasting, and 3 days(day and night) are equal to forty days(see Sha'ar Ruah HaKodesh Tikkun 1 page 6b, introduction to Sefer Beniyahu BenYehoida and Evn HaShoham hilchot teshuva siman 1).
Also many of the Kabbalistic Yeshivot in Jerusalem host tikkunim on Mondays and Thursdays in which, following the teachings of the RaShaSh and the Ben Ish Hai(see Lashon Hakhamim) the various fasts can be redeemed through tzedaka for those who are unable to fast.
with added option ( ת"ת )
is the initials of the parshas:
Shmos Vaeira Bo Beshalach Yisro Mishpatim (then optionally, Terumah Tetzaveh). So that makes it a period of 6 (or 8) weeks in the wintertime. It generally fills the a gap in the Jewish calendar post-Chanukah, pre-Purim. Of course the word "shovevim" means "wayward", as in "come back, wayward children!"
It's traditionally considered a time (especially in Hassidic communities) to focus on the observance of commandments related to marital intimacy.
In many communities across the gamut of Orthodoxy, refresher/review courses in taharat hamishpacha (family purity) are offered during this time.
I don't know what the oldest source for the backgrounds of "shovevim" are, but that's how it's done today.
In the Hassidic community of Satmar, it is a time for direct confrontation with one's baser desires, and sermons during this period will bring this up explicitly. There's the story of some fellows from the Skver Hassidic community (whose attitude is to focus on other things instead) going to Satmar during this period and hearing what was to them quite a shocking earful!
Regarding earliest source: Long before the Kav hayashar was born, the ShLo"H (R Yeshayah haLevi Horowitz circa 1560) wrote all about shovavim. You can find his rather simple and straightforward explanation of it and it's connection to Teshuva in his intro to the beginning of his exposition on parshat Shemot in the the sefer Shnei Luchos haBris, section called "Torah Sh'bichsav". Fabulous stuff.