Takenobu Nakao

Time evolution of Gaussian-type initial conditions associated with the Davey - Stewartson equations

The Cauchy problem of the Davey - Stewartson equations with non-trivial boundaries is studied. Initial conditions for the equations are chosen to have Gaussian-type envelope shapes, and the time evolution is investigated both theoretically and numerically. It is found that an initial packet grows and oscillates radiating ripples, then a localized structure called a dromion appears asymptotically. It is also observed that the ripples run away mainly along the mean flows. The results of numerical simulations and the analysis by the inverse scattering transform show good agreement with each other.