Solitary waves in a non-integrable FPU lattice

I will present a new semi-analytical solution describing discrete solitary waves in non-integrable FPU lattice with piecewise quadratic potential. The solution can be expressed in the form of an infinite series with coefficients satisfying a set of explicitly known transcendental equations. The parameter range is sufficiently broad to cover the whole spectrum of known behaviors from the delocalized solutions in the weakly nonlinear limit to the highly localized strongly discrete solitary waves where only one particle moves at a time. Joint work with Lev Truskinovsky.