Counterpropagating Two-Soliton Solutions in the FPU Lattice

Abstract

We study the interaction of small amplitude, long wavelength solitary waves in the Fermi-Pasta-Ulam model with general nearest-neighbor interaction potential. We establish global-in-time existence and stability of counter-propagating solitary wave solutions. These solutions are close to the linear superposition of two solitary waves for large positive and negative values of time; for intemediate values of time these solutions describe the interaction of two counterpropagating pulses. These solutions are stable with respect to perturbations in ${\ell }^2$ and asymptotically stable with respect to perturbations which decay exponentially at spatial $\pm \infty$.}

arXiv comment32 pages

References in corpus (1)

• Asymptotic stability of lattice solitons in the energy space

Cited by in corpus (14)

• Characterizing Traveling Wave Collisions in Granular Chains Starting from Integrable Limits: the case of the KdV and the Toda Lattice
• Continuous approximation of breathers in one and two dimensional DNLS lattices
• Asymptotic stability of breathers in some Hamiltonian networks of weakly coupled oscillators
• An averaging theorem for FPU in the thermodynamic limit
• KdV waves in atomic chains with nonlocal interactions
• Asymptotic two-soliton solutions in the Fermi-Pasta-Ulam model
• Existence and continuous approximation of small amplitude breathers in 1D and 2D Klein--Gordon lattices
• Micropteron traveling waves in diatomic Fermi-Pasta-Ulam-Tsingou lattices under the equal mass limit
• Nonlinear waves in Newton's cradle and the discrete p-Schroedinger equation
• High-energy waves in superpolynomial FPU-type chains
• Solitary waves in atomic chains and peridynamical media
• Asymptotic stability of N-solitons of the FPU lattices
• N-soliton states of the FPU lattices
• Exit manifolds for lattice differential equations