Rogue Wave Solutions And Spatial Temporal Structures For Two Types Nonlinear Evolution Equations

As a kind of complex nonlinear motion behaviour, the applied research for rogue waves has attracted more and more attention. And it has becoming one of the frontier in nonlinear science research. Rogue waves have wide applications in many fields, such as the oceanography, nonlinear optics, and plasma physics. Two types of nonlinear evolution equations are mainly investigated by using the method of generalized Darboux transformation(gDT) in this paper, one is the higher-order nonlinear Schr?dinger equation:and the other is the derivative nonlinear Schr?dinger equation:2=0 t xx xiu +u +i u u,(2) also called the Chen-Lee-Liu(CLL) equation. For eq.(1), the gDT matrix is constructed from the limiting technique. Under the action of this transformation, the n th-order rogue wave solutions with 2n +1free complex parameters are constructed. We have discussed the solutions dynamics in detail and classified them according to the spatial–temporal structures. Moreover, the nonlinear compression effects on the rogue wave solutions are compared and analyzed. Next, through the similar method, we have constructed calculation formulas with high complexity for the n th-order rational solitons and the n th-order rogue waves of eq.(2). At last, the 1-st to the 2-nd order rogue wave solutions are obtained via some simplification technique in integration.