Weierstrass's criterion and compact solitary waves

Abstract

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.

4 pages

References in corpus (2)

• Solitary and compact-like shear waves in the bulk of solids
• Nonlinear transverse waves in deformed dispersive solids

Cited by in corpus (8)

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• Peakompactons: Peaked compact nonlinear waves