Symmetric vibrations of higher dimensional nonlinear wave equations

• Nemanja Kosovalic ^[2] ; Brian Pigott ^[1]
  1. [1] Wofford College

     Wofford College

     Estados Unidos

     
  2. [2] Data Science Practice, USA
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 28, Nº. 3, 2022
• Idioma: inglés
• Enlaces
  • Texto completo (pdf)
• Resumen

  • We prove a result characterizing conditions for the existence and uniqueness of solutions of a certain Diophantine equation, then using techniques from equivariant bifurcation theory, we apply the result to prove symmetric Hopf bifurcation type theorems for both dissipative and non-dissipative autonomous wave equations, for a large set of spatial dimensions. For the latter only the classical implicit function theorem is used. The set of admissible spatial dimensions is the union of the perfect squares together with finitely many non-perfect squares.