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Blow-up scenario for a generalized Camassa–Holm equation with both quadratic and cubic nonlinearity

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ABSTRACT In this paper, we mainly devote to study an integrable generalized Camassa–Holm equation with both quadratic and cubic nonlinearity proposed by Xia, Qiao and Li [An integrable system with… Click to show full abstract

ABSTRACT In this paper, we mainly devote to study an integrable generalized Camassa–Holm equation with both quadratic and cubic nonlinearity proposed by Xia, Qiao and Li [An integrable system with peakon, complex peakon, weak kink, and kink-peakon interactional solutions. Commun Nonlinear Sci Numer Simul. 2018;63:292–306]. By overcoming the difficulties cased by the complicated mixed nonlinear structure, we present a precise blow-up scenario and some new blow-up results for strong solutions under different initial data.

Keywords: equation quadratic; camassa holm; quadratic cubic; blow; holm equation; generalized camassa

Journal Title: Applicable Analysis
Year Published: 2019

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