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Weierstrass's criterion and compact solitary waves.

Michel Destrade1, Giuseppe Gaeta, Giuseppe Saccomandi

  • 1Institut Jean Le Rond d'Alembert, UMR 7190, CNRS, Université Pierre et Marie Curie, 4 Place Jussieu, Case 162, 75252 Paris Cedex 05, France. destrade@lmm.jussieu.fr

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|May 16, 2007
PubMed
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A generalized Weierstrass theory identifies differential equations supporting solitary waves. This method reveals bulk shear waves in continuum mechanics for specific constitutive laws.

Area of Science:

  • Classical mechanics
  • Continuum mechanics
  • Differential equations

Background:

  • Weierstrass's theory is a standard qualitative tool for analyzing single degree of freedom equations.
  • It is widely used in classical mechanics and featured in numerous textbooks.
  • Existing methods are limited in identifying specific types of wave solutions.

Purpose of the Study:

  • To generalize Weierstrass's theory for identifying differential equations.
  • To explore the existence of compact and semicompact traveling solitary waves.
  • To connect these findings to bulk shear waves in continuum mechanics.

Main Methods:

  • Generalization of Weierstrass's theory.
  • Analysis of differential equations for solitary wave solutions.

Related Experiment Videos

  • Application of continuum mechanics principles.

    • Main Results:

    • A simple generalization of Weierstrass's theory successfully identifies differential equations.
    • The study confirms the existence of compact and semicompact traveling solitary waves.
    • These differential equations model bulk shear waves for specific constitutive laws.

    Conclusions:

    • The generalized Weierstrass theory provides a powerful tool for identifying solitary wave solutions.
    • This approach offers new insights into wave propagation in materials.
    • The findings have implications for understanding shear waves in continuum mechanics.