Nanoptera in a Period-2 Toda Chain

Abstract

We study asymptotic solutions to a singularly-perturbed, period-2 Toda lattice and use exponential asymptotics to examine `nanoptera', which are nonlocal solitary waves with constant-amplitude, exponentially small wave trains. With this approach, we isolate the exponentially small, constant-amplitude waves, and we elucidate the dynamics of these waves in terms of the Stokes phenomenon. We find a simple asymptotic expression for the waves, and we study configurations in which these waves vanish, producing localized solitary-wave solutions. In the limit of small mass ratio, we derive a simple anti-resonance condition for the manifestation these wave-free solutions.

arXiv comment31 journal pages

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Cited by in corpus (9)

• Nanopteron solutions of diatomic Fermi-Pasta-Ulam-Tsingou lattices with small mass-ratio
• Standing lattice solitons in the discrete NLS equation with saturation
• Topological Toda lattice and nonlinear bulk-edge correspondence
• Micropteron traveling waves in diatomic Fermi-Pasta-Ulam-Tsingou lattices under the equal mass limit
• Nanoptera in nonlinear woodpile chains with zero precompression
• Nanoptera In Higher-Order Nonlinear Schrödinger Equations: Effects Of Discretization
• A survey on asymptotic stability of ground states of nonlinear Schrodinger equations II
• Nanoptera and Stokes Curves in the 2-Periodic Fermi-Pasta-Ulam-Tsingou Equation
• Nanoptera in weakly nonlinear woodpile and diatomic granular chains