Asymptotic analysis of small energy breathers for the nonlinear Klein-Gordon equation

2025/11/25 by Kowalczyk, Michał, Martel, Yvan
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Photonic Systems #Nonlinear Waves and Solitons

paper · doi:10.48550/arxiv.2511.20553

openalex publication_date 2025/11/25 · openalex created_date 2025/11/28 · openalex updated_date 2026/07/28

Abstract

For a class of nonlinear Klein-Gordon equations, we prove that in the small energy limit, any sequence of breathers decomposes into a finite sum of decoupled, periodically modulated canonical solitons. Each of these solitons is asymptotically equal to an explicit sine-Gordon breather and the distance between them grows to infinity as the energy decreases to 0. Finally we prove that none of these breathers is centered in a bounded set provided that a certain non resonance condition holds.

Citations

• Asymptotic stability of the sine-Gordon kink
• Kink dynamics under odd perturbations for (1+1)-scalar field models with one internal mode
• Asymptotic stability of the sine-Gordon kink under odd perturbations
• A uniqueness result for the Sine-Gordon breather
• On modified scattering for 1D quadratic Klein-Gordon equations with\n non-generic potentials
• Long-time asymptotics and stability for the sine-Gordon equation
• Asymptotics for 1D Klein-Gordon Equations with Variable Coefficient Quadratic Nonlinearities
• Soliton dynamics for the 1D NLKG equation with symmetry and in the absence of internal modes
• Small Generalized Breathers with Exponentially Small Tails for Klein-Gordon Equations
• Resonances, radiation damping and instabilitym in Hamiltonian nonlinear wave equations
• Exact Solution of the Sine-Gordon Equation for Multiple Collisions of Solitons

Related

• Breather continuation from infinity in nonlinear oscillator chains
• Existence, linear stability and long-time nonlinear stability of Klein-Gordon breathers in the small-amplitude limit
• Small Generalized Breathers with Exponentially Small Tails for Klein-Gordon Equations
• Existence of breathers in nonlinear Klein-Gordon lattices
• Stability of Breathers for a Periodic Klein-Gordon Equation