Double-humped states in the nonlinear Schrödinger equation with a random potential

The role of double-humped states in spreading of wave packets for the nonlinear Schrödinger equation (NLSE) with a random potential is explored and the spreading mechanism is unraveled. Comparison to an NLSE with a double-well potential is made. There are two independent effects of the nonlinearity on the double-humped states for the NLSE: coupling to other states and destruction. The interplay between these effects is discussed.

Figure 1

(Color online) A pair of double-humped states for the linear system (2). The states are marked with blue solid line and green dashed line.

Figure 2

(Color online) Correlation between $R$ and ${\beta }_c$ (blue asterisks).

Figure 3

(Color online) The second moment as function of time for a representative double-humped (solid blue) and broken (dashed green) realizations for wave packets started in the vicinity of $O$.