Taking the coupled KdV system as a simple example, analytical and nonsingular complexiton solutions are firstly discovered in this letter for integrable systems. Additionally, the analytical and nonsingular positon-negaton interaction solutions are also firstly found for S-integrable model. The new analytical positon, negaton and complexiton solutions of the coupled KdV system are given out both analytically and graphically by means of the iterative Darboux transformations.Comment: 16 pages, 8 figure

A new Darboux transformation is presented for the Hirota-Satsuma coupled KdV system. It is shown that this Darboux transformation can be constructed by means of two methods: Painlevé analysis and reduction of a binary Darboux transformation. By iteration of the Darboux transformation, the Grammian type solutions are found for the coupled KdV system.

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New exact solutions with an arbitrary function for the (n + 1)-dimensional double sinh-Gordon equation are studied by means of auxiliary solutions of the cubic nonlinear Klein-Gordon (CNKG) fields. By a proper selection of the arbitrary function and the appropriate solutions of the CNKG systems, new wave solutions including periodic-kink like waves, periodic-solitoffs and periodic waves are obtained explicitly.

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