The descriptor "Long period variables" covers a very diverse group of stars whose main characteristics are: a) variability is caused by pulsation in the star, and b) periods or timescales are weeks, months, years, or longer. There's great variety among the stars that fall into that description, with a variety of physical characteristics given. In general, the LPVs are evolved stars, well beyond the stellar main sequence, and headed toward the ends of their lives as stars.
From a purely phenomenological standpoint, it's worth repeating the variable star classifications developed for the General Catalogue of Variable Stars. Stellar classes falling under the LPV umbrella are included below.
L Slow irregular variables. The light variations of these stars show no
evidence of periodicity, or any periodicity present is very poorly
defined and appears only occasionally. Like for the type I, stars are
often attributed to this type because of being insufficiently studied.
Many type L variables are really semiregulars or belong to other types.
LB Slow irregular variables of late spectral types (K, M, C, S); as a
rule, they are giants (CO Cyg). This type is also ascribed, in
the GCVS, to slow red irregular variables in the case of unknown
spectral types and luminosities.
LC Irregular variable supergiants of late spectral types having amplitudes
of about 1 mag in V (TZ Cas).
M Mira (Omicron) Ceti-type variables. These are long-period variable
giants with characteristic late-type emission spectra (Me, Ce, Se) and
light amplitudes from 2.5 to 11 mag in V. Their periodicity is
well pronounced, and the periods lie in the range between 80 and
1000 days. Infrared amplitudes are usually less than in the
visible and may be <2.5 mag. For example, in the K band they
usually do not exceed 0.9 mag. If the amplitudes exceed 1 - 1.5
mag , but it is not certain that the true light amplitude exceeds 2.5
mag, the symbol "M" is followed by a colon, or the star is
attributed to the semiregular class with a colon following the
symbol for that type (SR).
RV Variables of the RV Tauri type. These are radially pulsating
supergiants having spectral types F-G at maximum light and K-M at
minimum. The light curves are characterized by the presence of
double waves with alternating primary and secondary minima that
can vary in depth so that primary minima may become secondary and
vice versa. The complete light amplitude may reach 3-4 mag in V.
Periods between two adjacent primary minima (usually called formal
periods) lie in the range 30-150 days (these are the periods
appearing in the Catalogue). Two subtypes, RVA and RVB, are
RVA RV Tauri variables that do not vary in mean magnitude (AC Her);
RVB RV Tauri variables that periodically (with periods from 600 to
1500 days and amplitudes up to 2 mag in V) vary in mean
magnitude (DF Cyg, RV Tau).
SR Semiregular variables, which are giants or supergiants of intermediate
and late spectral types showing noticeable periodicity in their
light changes, accompanied or sometimes interrupted by various
irregularities. Periods lie in the range from 20 to >2000 days,
while the shapes of the light curves are rather different and
variable, and the amplitudes may be from several hundredths to
several magnitudes (usually 1-2 mag in V).
SRA Semiregular late-type (M, C, S or Me, Ce, Se) giants displaying
persistent periodicity and usually small (<2.5 mag in V) light
amplitudes (Z Aqr). Amplitudes and light-curve shapes generally
vary and periods are in the range of 35-1200 days. Many of these
stars differ from Miras only by showing smaller light amplitudes;
SRB Semiregular late-type (M, C, S or Me, Ce, Se) giants with poorly
defined periodicity (mean cycles in the range of 20 to 2300 days)
or with alternating intervals of periodic and slow irregular changes,
and even with light constancy intervals (RR CrB, AF Cyg). Every star
of this type may usually be assigned a certain mean period
(cycle), which is the value given in the Catalogue. In a number
of cases, the simultaneous presence of two or more periods of
light variation is observed;
SRC Semiregular late-type (M, C, S or Me, Ce, Se) supergiants (Mu Cep) with
amplitudes of about 1 mag and periods of light variation from 30 days to
several thousand days;
SRD Semiregular variable giants and supergiants of F, G, or K spectral
types, sometimes with emission lines in their spectra. Amplitudes
of light variation are in the range from 0.1 to 4 mag, and the range of
periods is from 30 to 1100 days (SX Her, SV UMa).
A little more about the Alphabet Soup...
AAVSO observer and former Councillor Kate Hutton wrote an article for this website to explain in greater detail the physics behind the major classes of variable star. Click the link above to learn more about the LPVs!