Weierstrass's criterion and compact solitary waves

Michel Destrade (1) , Giuseppe Gaeta (2) , Giuseppe Saccomandi (3)

1 LMM - Laboratoire de modélisation en mécanique
2 Dipartimento di Matematica
3 Dipartimento di Ingegneria dell'Innovazione

Weierstrass's theory is a standard qualitative tool for single degree of freedom equations, used in classical mechanics and in many textbooks. In this Brief Report we show how a simple generalization of this tool makes it possible to identify some differential equations for which compact and even semicompact traveling solitary waves exist. In the framework of continuum mechanics, these differential equations correspond to bulk shear waves for a special class of constitutive laws.

Domaines: Mécanique des solides [physics.class-ph]

Michel Destrade, Giuseppe Gaeta, Giuseppe Saccomandi. Weierstrass's criterion and compact solitary waves. Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, 2007, 75, pp.047601. ⟨10.1103/PhysRevE.75.047601⟩. ⟨hal-00192429⟩