Solitons in elastic solids (1938–2010). (English) Zbl 1272.74364

Summary: Solitons in solids are much less studied than in fluids or in optics although the seminal Fermi-Pasta-Ulam numerical experiment and its interpretation by Kruskal et al. indeed belong to this framework. An inquisitive observer and then an active participant for almost forty years, the author presents here the various developments that took place over this period in the solid mechanics and dynamics of lattices and/or structural members, as also the original results that followed thereby. Most of the solutions obtained deviate from standard ones as the physical systems deduced from first principles generally are not exactly integrable. The emphasis is placed on the peculiarities of the solutions in terms of analytical expressions, their interpretation, and their eventual representation as quasi-particles in steady (inertial) or accelerated motion.


74J35 Solitary waves in solid mechanics
74-02 Research exposition (monographs, survey articles) pertaining to mechanics of deformable solids
74-03 History of mechanics of deformable solids
01A60 History of mathematics in the 20th century
01A61 History of mathematics in the 21st century
Full Text: DOI Link


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