A new integrable equation with no smooth solitons

In this paper, we propose a new completely integrable equation:m_t = frac(1, 2) fenced(frac(1, m²))_xxx - frac(1, 2) fenced(frac(1, m²))_x,which has no smooth solitons. This equation is shown to have bi-Hamiltonian structure and Lax pair, which imply integrability of the equation. Studying this new equation, we develop two new kinds of soliton solutions under the inhomogeneous boundary condition lim_{| x | → ∞} m = B where B is nonzero constant. One is continuous and piecewise smooth "W/M"-shape-peaks solitary solution and the other one-single-peak soliton. The two new kinds of peaked solitons can not be written as the regular type peakon: c e^{- | x - ct |}, where c is a constant. We will provide graphs to show those new kinds of peaked solitons.