General \(N\)-dark-dark solitons in the coupled nonlinear Schrödinger equations. (English) Zbl 1244.35137
Summary: \(N\)-dark-dark solitons in the integrable coupled NLS equations are derived by the KP-hierarchy reduction method. These solitons exist when nonlinearities are all defocusing, or both focusing and defocusing nonlinearities are mixed. When these solitons collide with each other, energies in both components of the solitons completely transmit through. This behavior contrasts collisions of bright-bright solitons in similar systems, where polarization rotation and soliton reflection can take place. It is also shown that in the mixed-nonlinearity case, two dark-dark solitons can form a stationary bound state.
MSC:
| 35Q55 | NLS equations (nonlinear Schrödinger equations) |
| 35C08 | Soliton solutions |
| 35Q51 | Soliton equations |
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