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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: \[ u_t- u_{txx}+ 4uu_x= 3u_xu_{xx}+ uu_{xxx}, \quad t>0,\;x\in \mathbb R, \]
\[ u(0,x)= u_0(x), \quad x\in \mathbb R,\qquad u(t,x+1)= u(t,x), \quad t\geq 0,\;x\in \mathbb R. \]

MSC:

35Q58 Other completely integrable PDE (MSC2000)
35Q53 KdV equations (Korteweg-de Vries equations)
35G25 Initial value problems for nonlinear higher-order PDEs
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