RT journal article
T1 Conserved norms and related conservation laws for multi-peakon equations
A1 Recio Rodríguez, Elena
A1 Anco, Stephen C.
A2 Matemáticas
K1 peakon equation
K1 conserved norm
K1 conservation law
AB All nonlinear dispersive wave equations in the general classm_t + f (u, u_x)m + (g(u, u_x)m)_x = 0 are known to possess multi-peakonweak solutions. A classification is presented for families of multi-peakonequations in this class that possess conserved momentum; conserved H^1 normof u; conserved H^2 norm of u; conserved L^2 norm of m; related conservationlaws. The results yield, among others, two interesting wide families ofequations: m_t + 2u_xh(u, u_x)m + u(h(u, u_x)m)_x = 0 for which the H^1 norm of uis conserved; m_t − (1/2)*u_xh'(u)m + (h(u)m)_x = 0 for which the L^2 norm of m isconserved. The overlap of these two families yields a singular equation whichis nevertheless found to possess both smooth solitary wave solutions andpeakon travelling wave solutions.
SN 1751-8121
YR 2018
FD 2018
LK http://hdl.handle.net/10498/33283
UL http://hdl.handle.net/10498/33283
LA eng
DS Repositorio Institucional de la Universidad de Cádiz
RD 11-nov-2026