The nonlinear evolution of Kelvin–Helmholtz instability is examined in 2+1 dimensions in the context of magnetohydrodynamics. When the velocity difference U is less than the critical velocity Uc, the equation governing the amplitude evolves into a self-focusing singularity. The self-focusing of waves predominates at short wavelengths, is directionally dependent, and also depends sensitively on the strength of the applied magnetic field. The minimum velocity that allows the existence of self-focusing increases with increasing magnetic field strength. The explosive instability at the second-harmonic resonance is also investigated.