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Global existence for a new periodic integrable equation. (English) Zbl 1033.35121
Summary: We establish the local well-posedness for a new periodic integrable equation $$\alignat2 &u_t- u_{txx}+ 4uu_x= 3u_x u_{xx}+ uu_{xxx},\quad &&t> 0,\ x\in\Bbb R,\\ & u(0,x)= u_0(x),\quad &&x\in\Bbb R,\\ & u(t, x+1)= u(t,x),\quad &&t\ge 0,\ x\in\bbfR.\endalignat$$ We show that the equation has classical solutions that blowup in finite time as well as classical solutions which exist globally in time.

MSC:
35Q58Other completely integrable PDE (MSC2000)
35B40Asymptotic behavior of solutions of PDE
35B10Periodic solutions of PDE
35B30Dependence of solutions of PDE on initial and boundary data, parameters
37K10Completely integrable systems, integrability tests, bi-Hamiltonian structures, hierarchies
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References:
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