On the giant magnon and spike solutions for strings on AdS$_3\times$ S$^3$

Understand

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.