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Rogue Wave Solutions To Integrable System By Darboux Transformation, Xin Kou

Graduate College Dissertations and Theses

The Darboux transformation is one of the main techniques for finding solutions of integrable equations. The Darboux transformation is not only powerful in the construction of muilti-soliton solutions, recently, it is found that the Darboux transformation, after some modification, is also effective in generating the rogue wave solutions. In this thesis, we derive the rogue wave solutions for the Davey-Stewartson-II (DS-II) equation in terms of Darboux transformation. By taking the spectral function as the product of plane wave and rational function, we get the fundamental rogue wave solution and multi-rogue wave solutions via the normal Darboux transformation. Last but not …