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Home - ActivitiesIn this talk, we report our recent work on the genus two KdV soliton gases and their long-time asymptotics. This work employs the Riemann-Hilbert problem to provide a comprehensive analysis of the asymptotic behavior of the high-genus KdV soliton gases. It is demonstrated that the two-genus soliton gas is related to the two-phase Riemann-Theta function as x→+∞, and approaches to zero as x→−∞. Additionally, the long-time asymptotic behavior of this two-genus soliton gas can be categorized into five distinct regions in the x-t plane, which from left to right are rapidly decay, modulated one-phase wave, unmodulated one-phase wave, modulated two-phase wave, and unmodulated two-phase wave. Moreover, an innovative method is introduced to solve the model problem associated with the high-genus Riemann surface, leading to the determination of the leading terms, which is also related with the multi-phase Riemann-Theta function. A general discussion on the case of arbitrary N-genus soliton gas is also presented. This is a joint work with Dinghao Zhu and Xiaodong Zhu.