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Global weak solutions for a new periodic integrable equation with peakon solutions. (English) Zbl 1059.35149
Summary: We prove the existence of global weak solutions the following new periodic integrable equation with peakon solutions: $$u_t- u_{txx}+ 4uu_x= 3u_xu_{xx}+ uu_{xxx}, \quad t>0,\ x\in \Bbb R,$$ $$u(0,x)= u_0(x), \quad x\in \Bbb R,\qquad u(t,x+1)= u(t,x), \quad t\geq 0,\ x\in \Bbb R.$$

35Q58Other completely integrable PDE (MSC2000)
35Q53KdV-like (Korteweg-de Vries) equations
35G25Initial value problems for nonlinear higher-order PDE
Full Text: DOI
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