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Maxwell's equations are four equations known to Maxwell; but it seems to me that they are GFAM's (Gauss-Faraday-Ampere-Maxwell's) Equations.

Why are they then called only Maxwell's Equations!?

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Because Maxwell discovered that every other know law of electromagnetism could be derived starting from those four laws. He didn't discover the laws, but he did discover their significance. –  David H Mar 8 at 16:13
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Also, Maxwell actually knew these laws as a set of 20 coupled partial differential equations, not four vector equations, because vector notation wasn't invented until about 40 years after Maxwell. –  David H Mar 8 at 16:19
    
How many equations can you list whose names combine the name of four physicists? –  Drux Mar 8 at 18:07
    
@Drux I can name at least one that combines five physicists: the Bogoliubov–Born–Green–Kirkwood–Yvon hierarchy of equations, a.k.a. the BBGKY hierarchy. :) –  David H Mar 8 at 19:01
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added point: Maxwell himself would never have used the name "Maxwell equations", nor would almost certainly anyone else during his time. He didn't nor does he "own" them, he's merely honoured by his name being used to refer to them. –  jwenting Mar 8 at 19:11
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1 Answer 1

In the words of one Richard Feynman, from Chapter 28 of The Feynman Lectures in Physics Vol. 1:

Maxwell noted that the equations for the laws that had been discovered up to this time were mutually inconsistent when he tried to put them together, and in order for the whole system to be consistent he had to add another term to the equations. With this new term came an amazing prediction, which was that a part of the electric and magnetic fields would fall off much more slowly with the distance than the inverse square, namely, inversely as the first power of the distance! And so he realized that electric currents in one place can affect other charges far away, and he predicted the basic effects with which we are familiar today - radio transmission, radar, and so on.

This additional term to Ampere's Law is discussed in the Wikipedia article on Maxwell's Equations.

So yes, the consolidation of the four separate laws discovered by Gauss, Faraday and Ampere very much is a contribution unique to Maxwell, though individual laws still carry the names of their original discoverers, and are taught in that way in elementary physics curricula.

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The Feynman Lectures link I pointed to above is broken, and I have sent a message to the webmaster in that regard. I will update once I hear back from him. However, every Physics library worthy of the name will carry at least one copy of the three volumes, as Feynman's insights into modern physics have barely aged since his original presentation 50 years ago. –  Pieter Geerkens Mar 8 at 17:09
    
Links to Feynman Lectures site now working again. –  Pieter Geerkens Mar 8 at 19:38
    
s/fa awa/far away –  Lohoris Mar 8 at 20:51
    
Oh, sorry. There's a typo: "can affect other charges fa awa" should be "can affect other charges far away" ;) –  Lohoris Mar 8 at 22:46
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Corrected; thank you. I didn't realize you were old enough to know sed commands. ;-) –  Pieter Geerkens Mar 9 at 0:31
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