Abstract
We show that the quasi-integrability concept holds for the modified defocusing NLS model with dark soliton solutions and it exhibits the new feature of an infinite sequence of alternating conserved and asymptotically conserved charges. For the special case of two dark soliton solutions, where the field components are eigenstates of a space-reflection symmetry, the first four and the sequence of even order charges are exactly conserved in the scattering process of the solitons. We perform extensive numerical simulations and consider the scattering of dark solitons for the cubic-quintic NLS model with potential and the saturable type potential satisfying , q ∈ ℤ+, with a deformation parameter ϵ ∈ ℝ and I = |ψ|2.. The saturable NLS supports elastic scattering of two soliton solutions for a wide range of values of {η, ϵ, q}. Our results may find potential applications in several areas of non-linear science, such as the Bose-Einstein condensation.
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