We study a family of equations defined on the space of tensor densities of weight on the circle and introduce two integrable PDE. One of the equations turns out to be closely related to the inviscid Burgers equation while the other has not been identified in any form before. We present their Lax pair formulations a…
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Multipeakons are special solutions to the Camassa-Holm equation described by an integrable geodesic flow on a Riemannian manifold. We present a bi-Hamiltonian formulation of the system explicitly and write down formulae for the associated first integrals. Then we exploit the first integrals and present a novel approach…
Geometric tools study two- and threepeakons in Camassa-Holm equation.
problem Dynamics of peakon solutions in the Camassa-Holm equation.
method Geometric tools applied to prove asymptotic behavior and compute curvature.
result New proofs and curvature computations for two- and threepeakons.