We show the existence of waveforms of finite-energy (vector solitons) for a coupled nonlinear Schrödinger system with inhomogeneous coefficients. Furthermore, some of these solutions are approximated using a Newton-type iteration, combined with a collocation-spectral strategy to discretize the corresponding soliton equations. Some numerical simulations concerned with analysis of a collision of two oncoming vector solitons of the system are also performed.
We introduce a Newton’s iterative method to approximate periodic and nonperiodic travelling wave solutions of the Schrödinger-Benjamin-Ono system derived by M. Funakoshi and M. Oikawa. We analyze numerically the influence of the model’s parameters on these solutions and illustrate the collision of two unequal-amplitude solitary waves propagating with different speeds computed by using the proposed numerical scheme.
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