Abstract:The two-component Novikov equation is an integrable generalization of the Novikov equation, which has the peaked solitons in the sense of distribution as the Novikov and Camassa-Holm equations. In this paper, we prove the existence of the H 1-weak solution for the two-component Novikov equation by the regular approximation method due to the existence of three conserved densities. The key elements in our approach are some a priori estimates on the approximation solutions.
“…Over the last few years, various modifications and generalizations of the CH equation (1.1) have been introduced [4,5,27,39,45,55]. So it is of greatest to find such integrable CH-type equations with cubic and higher-order nonlinearity.…”
<p style='text-indent:20px;'>This paper is devoted to studying the dynamical stability of periodic peaked solitary waves for the generalized modified Camassa-Holm equation. The equation is a generalization of the modified Camassa-Holm equation and it possesses the Hamiltonian structure shared by the modified Camassa-Holm equation. The equation admits the periodic peakons. It is shown that the periodic peakons are dynamically stable under small perturbations in the energy space.</p>
“…Over the last few years, various modifications and generalizations of the CH equation (1.1) have been introduced [4,5,27,39,45,55]. So it is of greatest to find such integrable CH-type equations with cubic and higher-order nonlinearity.…”
<p style='text-indent:20px;'>This paper is devoted to studying the dynamical stability of periodic peaked solitary waves for the generalized modified Camassa-Holm equation. The equation is a generalization of the modified Camassa-Holm equation and it possesses the Hamiltonian structure shared by the modified Camassa-Holm equation. The equation admits the periodic peakons. It is shown that the periodic peakons are dynamically stable under small perturbations in the energy space.</p>
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