Coalescence of wavenumbers and exact solutions for a system of coupled nonlinear Schrodinger equations

An exact 2-soliton expression is obtained for the Manakov system, a special , coupled set of nonlinear Schrodinger equations. The solution permits diff erent asymptotic states for the components in the far field. A 'coalescence ' of wavenumbers is considered from the perspective of the Hirota bilinear operator. This is roughly equivalent to a double (or in general multiple) p ole solution in the language of the inverse scattering transform. Physicall y counterpropagating waves will occur. With the help of computer algebra so ftware a 3-soliton solution is derived. Coalescence of eigenvalues is inves tigated. Temporal modulation of the amplitude is observed.