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There are several definitions for the refraction coefficient. We adopt the definition found in A. C. Newell and J. V. Moloney, Nonlinear Optics (Addison-Wesley, Redwood City, Calif., 1992), Chap. 2. The relation among these different definitions is given in App. 5 of Ref. 29.
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33
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84894390993
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note
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1) ≪ O(1), strong interactions between two gray dark spatial solitons occur, which can be studied by the two-soliton solutions of the Kadomtsev-Petviashvili-I equation, a reduced form of NLS equation (7) in nearly one spatial dimension. For the derivation of the Kadomtsev-Petviashvili-I equation from the defocusing NLS equation, see Refs. 22 and 23.
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