Ultrasonic Kink-Solitons in Fermi-Pasta-Ulam Chains

– We use the sharp pulse method to perform numerical experiments aimed at exciting moving high energy strongly localized kink-solitons in the Fermi-Pasta-Ulam chain of anharmonic oscillators. An approximate analytical expression of the kink-soliton is derived. This is compatible with the fact that these objects move with ultrasonic velocities, proportional to stiffness. For low excitation energies our kink-solitons reduce to the well-known soliton solutions of the modified Korteweg de-Vries (KdV) equation. For high excitation energies kinksolitons acquire a compact support as it happens for KdV-like equations with nonlinear dispersive terms: P. Rosenau, Phys. Rev. Lett., 73, 1737, (1994). Introduction. – The interest in studying moving nonlinear localized excitations (solitons, kinks, etc.) is mainly motivated by the fact that they could be related to the transport properties of the system. In this connection, one dimensional lattices of anharmonic oscillators should be expecially mentioned because they can serve as a testing ground for nonlinear transport behavior. In particular, Fermi-Pasta-Ulam chains (FPU) [1] are characterized by a divergent heat conductivity [2]. This anomalous behavior could be explained by the presence of weakly damped linear long wavelength excitations but also by the existence of exact moving solitonic solutions in the nonlinear regime. Let us mention that invariance under the symmetry transformation that shifts the positions of all oscillators by the same amount relates FPU chain to a wide class of systems which share such continuous symmetries, e.g. quasi-one dimensional easy plane ferromagnets and antiferromagnets [3, 4], ferrimagnetic systems with spiral structures [5] and even quantum Hall double layer pseudo-ferromagnets [6]. Anomalous transport properties could appear for all the systems in this class. This makes extremely important to assess whether such properties could be related to the existence of moving localized solutions by analyzing in detail the case of the FPU model. Two types of numerical methods have been commonly used to study the time evolution of localized objects (both static and moving) in anharmonic lattices (see e.g. the review paper [7]): i) exact [7, 8] or approximate [9, 10] solutions are put initially onto the lattice and ii) modulational instability of zone-boundary modes is induced [11, 12, 13, 14, 15, 16]. The first