A Dispersive Regularization for the Modified Camassa--Holm Equation
نویسندگان
چکیده
منابع مشابه
Wave-breaking for the Weakly Dissipative Modified Camassa-Holm Equation
The equation (1) arises from an intrinsic (arc-length preserving) invariant planar curve flow in Euclidean geometry and it can be regarded as a Euclidean-invariant version of the Camassa-Holm equation in [1]. It has the form of a modified Camassa-Holm equation with cubic nonlinearity. By Fuchssteiner [2] and Olver and Rosenau[3], it can be derived as a new integrable system by applying the gene...
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The Camassa-Holm (CH) equation is a well-known integrable equation describing the velocity dynamics of shallow water waves. This equation exhibits spontaneous emergence of singular solutions (peakons) from smooth initial conditions. The CH equation has been recently extended to a two-component integrable system (CH2), which includes both velocity and density variables in the dynamics. Although ...
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Abstract. We consider the viscous Camassa-Holm equation subject to an external force, where the viscosity term is given by second order differential operator in divergence form. We show that under some mild assumptions on the viscosity term, one has global wellposedness both in the periodic case and the case of the whole line. In the periodic case, we show the existence of global attractors in ...
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has been extensively studied since the first systematic analysis in [5, 6]. Part of the attraction is the surprising complexity of the equation and its deep and nontrivial properties. To list a few of its peculiarities: The Camassa–Holm equation has a bi-Hamiltonian structure [16], it is completely integrable [5], and it has infinitely many conserved quantities [5]. Here we study the equation w...
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ژورنال
عنوان ژورنال: SIAM Journal on Mathematical Analysis
سال: 2018
ISSN: 0036-1410,1095-7154
DOI: 10.1137/17m1132756