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Referee: This paper really needs to be proof read by an English native or by someone fluent in English, because the number of grammatical errors is huge.

ÎÒÖ»ÄÜ»Ø: Sorry for our poor English. We have tried our best to improve the English writting.

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Over the Past decades£¬partially coherent beams have been extensively investigated and have found wide applications in many fields£¬such as free-space optical communications£¬material thermal processing by laser beam£¬laser scanning£¬inertial confinement fusion by laser£¬nonlinear optics and imaging applications. Recently£¬the characterization and propagation of partially coherent beams are topics of considerable interest. The partially coherent sources could produce the same far-field intensity distribution as a laser. Moreover, the partially coherent beams are demonstrated to have advantage over the spatially completely coherent beams. So here we further study of partially coherent pulsed beam  modulation instability.
When two or more optical fields having different wavelengths propagate simultaneously inside a medium, they interact with each other through the medium nonlinearity. The medium nonlinearity can also couple two fields through cross-phase modulation without inducing any energy transfer between them. The physical system please see G. P. Agrawal Nonlinear Fiber Optics, 3rd Edition.Our proposed equation (1), it applied to the two optical fields in Kerr medium, because his cross-phase modulation, so need to use the last one in equation (1) to describe.
As we discuss problems of two optical fields of partially coherent light, therefore, must be use the concept of the statistical average. The equation (1) of the further research on the reference [16]. The second page of the revised manuscript, we further described in equation (1).
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