Guha, P. Euler-Poincaré formalism of peakon equations with cubic nonlinearity. (English) Zbl 1345.35088 J. Gen. Lie Theory Appl. 9, No. 1, Article ID 1000225, 7 p. (2015). The paper addresses a recently introduced integrable equation with the cubic nonlinearity: \[ u_t - u_{xxt} + 4u^2u_x = 3uu_xu_{xx} + u^2u_{xxx}. \] This equation admits exact peakon solutions, in the form of localized pulses with a jump of the first derivative at the center. Integrable equations which give rise to peakon solutions were known before, but with quadratic nonlinear terms, such as the Camassa-Holm equation. The objective of the work is to analyze the Hamiltonian structure of the equation. It is demonstrated that the structure can be made equivalent to the Euler-Poincaré formulation. Reviewer: Boris A. Malomed (Tel Aviv) MSC: 35Q53 KdV equations (Korteweg-de Vries equations) 35Q35 PDEs in connection with fluid mechanics Keywords:Fokas-Qiao equation; bi-Hamiltonian structures; Novikov equation; Camassa-Holm equation PDFBibTeX XMLCite \textit{P. Guha}, J. Gen. Lie Theory Appl. 9, No. 1, Article ID 1000225, 7 p. (2015; Zbl 1345.35088) Full Text: Euclid