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Can we expect that Kasparov comes up with a new chess variant, like Fisher
did?

I just recalled that Kasparov actually already invented a kind of new chess
variant: 'Advanced Chess' (see e.g.
http://en.wikipedia.org/wiki/Advanced_Chess).

Since 1998, Advanced Chess (Chess with computer assistance) is played by
Grand-Masters in official Tournaments. There is not official rating,
although Anand is considered the number one in this variant, but Kramnik
defeated Anand in 2002. Kasparov is, playing Advanced Chess, in third or
fourth unnofficial position. Anand is a extremely strong player, precisely
against computer programs, and it seems it uses the programs in a better
way than his opponents, but as he said, you must play good Chess, if not,
computer aid is not enough.

We can´t expect to see other player as Kasparov for many years. He was,
possibly, the best Chess player of all the times.

Kasparov leaves us with an incredible legacy.  His five matches with Karpov
totaled 144 games.  We may never again see a champion play so many games at
the highest level.  Compare the career of one of his 'great
predecessors':

In 1927 Alexander Alekhine defeated World Chess Champion Jose Raul
Capablanca in a 34 game match (+6 =25 -3).  In 1929 he defeated FIDE World
Chess Champion Efim Bogoljubow in a 25 game 'unification match' (+11 =9
-5).   Again in 1934 he defeated Bogoljubow in a 26 game match (+8 =15
-3).  From 1928 to 1938 Alekhine played a total of eight games against
past and future world champions Botvinnik, Capablanca and Lasker.

Zurich 1934: 1 win (Lasker).

Nottingham 1936: 2 draws (Botvinnik and Lasker), 1 loss (Capablanca).

AVRO 1938: 1 win (Capablanca), 2 draws (Botvinnik and Capablanca), 1 loss
(Botvinnik).