1 results
Branching patterns of wave trains in mass-in-mass lattices
- Part of
-
- Journal:
- Proceedings of the Royal Society of Edinburgh. Section A: Mathematics , First View
- Published online by Cambridge University Press:
- 11 January 2024, pp. 1-27
-
- Article
-
- You have access
- HTML
- Export citation
-
We investigate the existence and branching patterns of wave trains in the mass-in-mass (MiM) lattice, which is a variant of the Fermi–Pasta–Ulam (FPU) lattice. In contrast to FPU lattice, we have to solve coupled advance-delay differential equations, which are reduced to a finite-dimensional bifurcation equation with an inherited Hamiltonian structure by applying a Lyapunov–Schmidt reduction and invariant theory. We establish a link between the MiM lattice and the monatomic FPU lattice. That is, the monochromatic and bichromatic wave trains persist near $\mu =0$
in the nonresonance case and in the resonance case $p:q$
where $q$
is not an integer multiple of $p$
. Furthermore, we obtain the multiplicity of bichromatic wave trains in $p:q$
resonance where $q$
is an integer multiple of $p$
, based on the singular theorem.
