Wave-breaking for the Weakly Dissipative Modified Camassa-Holm Equation
نویسندگان
چکیده
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 general method of tri-Hamiltonian duality to the bi-Hamiltonian representation of the modified Korteweg-de Vries equation. Later, it was obtained by Qiao [4] from the two-dimensional Eular equations. In [5] it was shown that equation (1) admits a Lax pair. In [1] it can be solved by the method of inverse scattering, its scaling limit equation satisfies the short-pulse equation. The original Camassa-Holm (CH) equation
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