What exactly are right movers and left movers in string theory? In string theory , What exactly are right movers and left movers ?Are they  waves propagating along the string to the right and to the left respectively ?
Can some-one please show me how to derive in details the general solution of the equation of motion for the string?
 A: I hope the instructors don't mind me posting their materials here but :
http://staff.science.uva.nl/~skenderi/string_theory_2012.html
The problem sets (which have solutions) walk you through the derivation of the equation of motion for the string (I'm assuming you refer to the derivation of the wave equation and then the derivation of the form $\vec X$ must take to solve that wave equation).  The left moving wave is just $\vec X(\tau + \sigma)$ part and the right moving wave is $\vec X(\tau -\sigma)$ part.
A: The solutions to the classical string equations of motion are given by the embedding functions as functions of the string world sheet parameters $(\sigma, \tau)$. The solutions are given in terms of arbitrary vector functions of $\sigma \pm \tau$. The positive sign are called right movers and the negative sign left movers. Being functions of this particular combination of parameters they represent wavelike oscillations propagating in opposite direction in the world sheet parameter space of the string. Left or right is just referring to the relative sign of the space-like and time-like word sheet parameters. You can think about them like the opposite traveling waves in an ordinary standing wave.
