  We study solutions for the rotating strings on the sphere with a background
NS-NS field and on the Anti-de-Sitter spacetime. We show the existence of
magnon and single spike solutions on R$\times$S$^2$ in the presence of constant
magnetic field as two limiting cases. We also study the solution for strings on
AdS$_3\times$ S$^3$ with Melvin deformation. The dispersion relations among
various conserved charges are shown to receive finite corrections due to the
deformation parameter. We further study the rotating string on AdS$_3 \times$
S$^3$ geometry with two conserved angular momenta on S$^3$ and one spin along
the AdS$_3$. We show that there exists two kinds of solutions: a circular
string solution and a helical string. We find out the dispersion relation among
various charges and give physical interpretation of these solutions.
