id author title date pages extension mime words sentence flesch summary cache txt ejde-341 Zhu, Min; Wang, Ying; Chen, Lei Curvature blow-up for the periodic CH-mCH-Novikov equation 2021 14 .pdf application/pdf 5914 337 88 Preliminaries To discuss the wave breaking phenomenon of the periodic CH-mCH-Novikov equation (1.1), we rewrite it as ut = −k1G ∗ (2uxm+ umx)− k2G ∗ ((u2 − u2x)m)x − k3G ∗ (u2mx + 3uuxm), t > 0, x ∈ S, u(0, x) = u0(x), x ∈ S, (2.1) where G(x) = cosh(x−[x]− 1 2 ) 2 sinh(1/2) , [x] represents the largest integer part of x, and G(x) is the fundamental solution of (1 − ∂2x)−1 on the unit circle S = R/Z, that is for any x ∈ S. Let G(x) = Λ1(x)+Λ2(x), where Λ1(x) = ex−[x]− 1 2 4 sinh( 1 2 ) and Λ2(x) [Λ1 ∗ (u− ux)3 − Λ2 ∗ (u+ ux)3] − k1[Λ2 ∗ (u2 + 1 2 u2x)− Λ1 ∗ (u2 + 1 2 u2x)], ûx ′ (t) = k1(û2 − 1 2 ûx 2 ) + k2( 1 3 û3 − ûûx2) + k3û 2 (û2 − ûx2) − ( k2 3 + k3 2 ) cache/ejde-341.pdf txt/ejde-341.txt