Nonlinear Sciences – Exactly Solvable and Integrable Systems
Scientific paper
1998-08-24
Inverse Problems 14 (1998) 1371-1383
Nonlinear Sciences
Exactly Solvable and Integrable Systems
15 pages, 5 figures, to appear in Inverse Problems
Scientific paper
10.1088/0266-5611/14/5/019
Using the nonlinear constraint and Darboux transformation methods, the (m_1,...,m_N) localized solitons of the hyperbolic su(N) AKNS system are constructed. Here "hyperbolic su(N)" means that the first part of the Lax pair is F_y=JF_x+U(x,y,t)F where J is constant real diagonal and U^*=-U. When different solitons move in different velocities, each component U_{ij} of the solution U has at most m_i m_j peaks as t tends to infinity. This corresponds to the (M,N) solitons for the DSI equation. When all the solitons move in the same velocity, U_{ij} still has at most m_i m_j peaks if the phase differences are large enough.
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