On a Negative Flow of the AKNS Hierarchy and Its Relation to a Two-Component Camassa-Holm Equation
نویسندگان
چکیده
منابع مشابه
Singular solutions of a modified two-component Camassa-Holm equation.
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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One of the many remarkable facts concerning the theory of integrable PDEs is that almost all these equations can be obtained as suitable reductions from (integrable) hierarchies living on loop-algebras. The main example is the Drinfeld-Sokolov reduction [12], leading from (the loop-algebra of) a simple Lie algebra g to the so-called generalized Korteweg-deVries (KdV) equations. It is well-known...
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This talk is focused on recent progress of studies for the Camassa-Holm equation. First, we will give a brief review on the derivations, well-posedness for the strong solution, blow-up phenomenon and existence of the weak solutions. Then, infinite propagation speed for the Camassa-Holm equation will be proved in the following sense: the corresponding solution u(x, t) with compactly supported in...
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ژورنال
عنوان ژورنال: Symmetry, Integrability and Geometry: Methods and Applications
سال: 2006
ISSN: 1815-0659
DOI: 10.3842/sigma.2006.070