Strictly supersonic solitary waves in lattices with second-neighbor interactions

Highlights: • Solitary waves in chains with competing interactions were studied analytically. • Some obtained solutions are of envelope type and involve two length scales. • There is a parameter range where solitary waves are strictly supersonic. • Higher-order quasicontinuum theories are necessary to capture these effects. -- Abstract: We consider a monatomic nonlinear mass–spring chain with first and second-neighbor interactions and show that there is a parameter range where solitary waves in this system are strictly supersonic. In these regimes standard quasicontinuum theories, targeting long-wave limits of lattice models, are not adequate since even weak strictly supersonic solitary waves are of envelope type and crucially involve a microscopic scale in addition to the mesoscopic scale of the envelope. To capture this effect in a continuum setting it is necessary to employ unconventional, higher-order quasicontinuum approximations carrying more than one length scale.