%0 Journal Article 
%A Recio Rodríguez, Elena
%A Anco, Stephen C.
%T Conserved norms and related conservation laws for multi-peakon equations
%D 2018
%@ 1751-8121
%U http://hdl.handle.net/10498/33283
%X All nonlinear dispersive wave equations in the general class
m_t + f (u, u_x)m + (g(u, u_x)m)_x = 0 are known to possess multi-peakon
weak solutions. A classification is presented for families of multi-peakon
equations in this class that possess conserved momentum; conserved H^1 norm
of u; conserved H^2 norm of u; conserved L^2 norm of m; related conservation
laws. The results yield, among others, two interesting wide families of
equations: m_t + 2u_xh(u, u_x)m + u(h(u, u_x)m)_x = 0 for which the H^1 norm of u
is conserved; m_t − (1/2)*u_xh'(u)m + (h(u)m)_x = 0 for which the L^2 norm of m is
conserved. The overlap of these two families yields a singular equation which
is nevertheless found to possess both smooth solitary wave solutions and
peakon travelling wave solutions.
%K peakon equation
%K conserved norm
%K conservation law
%~ Universidad de Cádiz