I know that one uses the accusative with suchen, e.g.
Ich suche einen Hund.
and of course the dative with nach etwas suchen, e.g.
Ich suche nach einem Hund.
What is the difference between these two expressions?
I know that one uses the accusative with suchen, e.g.
Ich suche einen Hund.
and of course the dative with nach etwas suchen, e.g.
Ich suche nach einem Hund.
What is the difference between these two expressions?
I think here is a slight difference. Let make it different:
Ich suche eine Frau.
has more the general meaning of looking for something in general, as if you are on online dating and just want to find someone.
This expression:
Ich suche nach einer Frau.
has a slight shift towards the meaning that you are looking for a specific person with which you have somehow lost contact.
For example, both can be used for a detective searching someone, but the second puts a little more emphasis that he is really looking for a specific person.
I think for the most part they are synonymous, especially considering that any statement could be rephrased using the noun and then we'd use "nach" regardless.
Ich bin auf der Suche nach...
There are situations where one fits better than the other though and a possible key is the etymology. "Zu suchen" is a cognate to "to seek" and that in itself is a rather strong and determined activity. Much more determined than searching. This determination or goal orientation if you will comes into play in sentences where "suchen" leans toward demanding.
Ich suche Hilfe, Schutz, Verständnis...
The version with "nach" would much more sound like you're actually searching for it as in turning over stones, wondering where help could be hiding. The pure "suchen" is closer to the seeking and thus a better fit in these situations
I seek help, protection, understanding
In most cases it's the same. but as Karl said in his answer, "nach etwas suchen" is sometimes more specific.
I would understand your example "Ich suche einen Hund." that way: You don't have a dog, but you want one, so you are searching for the right dog for you.
But "Ich suche nach einem Hund." could easily be understood that way: You have a dog, but it ran away, so you are searching for it.