Well-Posedness of a Hirota–Satsuma System Posed on a Half Line - Haiyan Lu (Journal of Mathematics)
This paper studies the initial boundary value problem of the Hirota–Satsuma system posed on the half line. ut−αuxxx+6uux=2βvvx,x>0,t>0,vt+vxxx+3uvx=0,x>0,t>0,ux,0=u0x,vx,0=v0x,x>0,u0,t=ft,v0,t=gt,t>0.. For −1/8<s<3/2,s≠1/2, we demonstrate that the abovementioned system is locally well-posed in Hsℝ×H1+sℝ by utilizing several analytic boundary forcing operators.