Is there any alternative to the "sed -i" command in Solaris?

Use ed. It's available on most platforms and it can edit your files in-place.
Since sed is based on ed the syntax for replacing patterns is similar:

ed -s infile <<\IN
,s/old/new/g
w
q
IN

If you cannot install GNU sed, use:

sed "s/foo/fooofoo/g" abc.txt >abc.tmp && mv abc.tmp abc.txt

This uses redirection to send the output of sed to a temporary file. If sed completes successfully, then this overwrites abc.txt with the temporary file.

As can be seen from the source code for GNU sed, this is exactly what sed -i does. So, this is just about as efficient as sed -i.

If there is a chance that abc.tmp already exists, then you may want to use mktemp or a similar utility to generate the unique name for the temporary.

If you want the equivalent of sed -i.bak, it's pretty simple.

Consider this script for GNU sed:

#!/bin/sh

# Create an input file to demonstrate
trap 'rm -r "$dir"' EXIT
dir=$(mktemp -d)
grep -v '[[:upper:][:punct:]]' /usr/share/dict/words | head >"$dir/foo"

# sed program - removes 'aardvark' and 'aardvarks'
script='/aard/d'

##########
# What we want to do
sed -i.bak -e "$script" "$dir"
##########

# Prove that it worked
ls "$dir"
cat "$dir/foo"

We can simply replace the marked line with

cp "$dir/foo" "$dir/foo.bak" && sed -e "$script" "$dir/foo.bak" >"$dir/foo"

This moves the existing file to be a backup, and writes a new file.

If we want the equivalent of

sed -i -e "$script" "$dir"  # no backup

then it's slightly more complex. We can open the file for reading as standard input, then unlink it, before directing sed's output to replace it:

( cp "$dir/foo" "$dir/foo.bak"; exec <"$dir/foo.bak"; rm "$dir/foo.bak"; exec sed -e "$script" >"$dir/foo" )

We do this in a sub-shell, so that our original stdin is still available after this. It's possible to switch inputs and switch back without a subshell, but this way seems clearer to me.

Note that we're careful to copy first, rather than creating a new foo file - this is important if the file is known by more than one name (i.e. has hard links) and you want to be sure that you don't break the links.