Cauchy matrix structure of the Mel’nikov model of long-short wave interaction  

作　　者：Hong-Juan Tian Da-Jun Zhang 

机构地区：[1]Department of Mathematics,Shanghai University,Shanghai 200444,China

出　　处：《Communications in Theoretical Physics》2020年第12期83-93,共11页理论物理通讯（英文版）

基　　金：supported by the NSF of China(Nos.11875040 and 11631007)。

摘　　要：We propose a systematic method to construct the Mel’nikov model of long–short wave interactions,which is a special case of the Kadomtsev–Petviashvili(KP)equation with self-consistent sources(KPSCS).We show details how the Cauchy matrix approach applies to Mel’nikov’s model which is derived as a complex reduction of the KPSCS.As a new result wefind that in the dispersion relation of a 1-soliton there is an arbitrary time-dependent function that has previously not reported in the literature about the Mel’nikov model.This function brings time variant velocity for the long wave and also governs the short-wave packet.The variety of interactions of waves resulting from the time-freedom in the dispersion relation is illustrated.

关 键 词：Mel’nikov model of long–short wave interaction Cauchy matrix approach self-consistent sources KP equation 

分 类 号：O175[理学—数学]