Combined control of Akhmediev breather frequency and rogue wave amplitude: An analytical approach

Abstract

We illustrate the analytical control of the Akhmediev breather frequency in BoseEinstein condensate in a time varying parabolic trap. This is achieved by varying Feshbach managed scattering length R(t) within the integrability framework. Recognizing the mathematical relation between R(t) and parabolic trap with the linear Schrödinger equation, we use isospectral Hamiltonian approach, which leads to a one parameter family of nonlinearity control functions, directly affecting the characteristic scales of the solution space, for the same trapping potential. The chirp equation and the trap equation being same, the phase of the wave for the obtained class of nonlinearity function remains identical. For explicating the general applications of the present approach, we exhibit breather frequency control in a number of cases, with asymptotically vanishing nonlinearity, for expulsive parabolic trap. Interestingly, the same procedure is found to provide a free parameter, which controls the Rogue wave amplitude.