On a nonlinear effect in the superconductivity theory

Based on the solution of the hydrodynamic equations and Maxwell's equations, we show that an external quasi-homogeneous magnetic field leads to the emergence of a secondary electric field that is resulted from a nonlinear effect over magnetic potential $\mathbf A$. This field is proved to exist in the region with a depth of $\delta/2$, where $\delta$ is the London penetration depth. The hydrodynamic flow velocity is estimated.