Collision Of Rogue Waves In Bose-Einstein Condensate

Rogue waves(RWs)also known as extreme waves or freak waves,are one of the most strange physical phenomena first originating from the vast ocean that appear suddenly and disappear without a trace.Because of the mystery and destructiveness of rogue waves,people have attracted great interest and have been studied them in many different systems.After a long period of research,it is found that the rogue wave is ubiquitous in nature,and can be controlled and excited to show up at a fixed time and location by some means.This may inspire the study of rogue waves at sea,so as to obtain methods to prevent them from destroying the ships and the equipment of exploiting oil fields at sea,so that it can produce economic benefits,so the research of the rogue wave has high value.We summarize the main work of the current rogue wave into two aspects: one is in the single component,multi-component,first-order rogue wave,high-order rogue wave and other aspects of the exact solution to solve,the other side is committed to produce first-order rogue wave,high-order rogue wave and some other properties in the experiment.However,it is difficult to solve the higher-order exact solution of the rogue wave,and it is not favorable to generate the rogue wave on the experiment,so it is urgent to find a simpler and easier method.Therefore,we came up with the idea of designing a scheme in which all physical parameters could be controlled in the system.In fact,we notice that the rogue waves can be excited and controlled to appear at a fixed time and location with the wide Gaussian initial condition.Based on these motivations,we consider that Bose-Einstein condensate is an ideal experimental platform,which can be described by the Gross-Pitaevskii(GP)equation of mean field approximation,and the interaction parameters can be manipulated experimentally such as population density and Feshbach resonance technique.In this report,we choose Gaussian wave packet with offset as the initial condition to numerically study the rogue wave collision events in one-dimensional two-component Bose-Einstein condensates,which means that we propose a simple and easy to implement scheme to generate higher order rogue waves.The results show that the successful excitation of second-order rogue waves depends on the location and time of the encounter of first-order rogue waves.Standard second-order rogue waves can be triggered only when the highest peaks of two rogue waves meet at the same location with the same time,and its structure is well agreement with the exact solution.In addition,we demonstrate that such results also applicable for the collision of subordinate order rogue waves.In this paper,the higher order rogue waves generated in two-component Bose-Einstein condensates and the effect of the offset and the interaction between the two components on the structure of the second-order rogue are studied under the mean field approximation.This work not only reveals the collision characteristics of rogue waves,but also provides a feasible scheme to generate higher order rogue waves for experimental implementation.It is hoped that this paper can provide new ideas for the study of rogue waves and Bose-Einstein condensates.