Abstract
Fermi-Pasta-Ulam (FPU) lattice known as a nonlinear lattice includes nonlinear terms explicitly. Therefore, we can evaluate nonlinear effects of FPU lattice straightforwardly. It includes, however, only the nearest neighbor interactions. In some cases, long range interaction plays an important role in dynamical properties in real crystals. We take the second nearest neighbor interactions into account in FPU lattice. We derive the nonlinear wave equation (modified Kortweg-de Vries – type equation) from the nonlocal FPU lattice as a continuum limit. Linear dispersion relationship of the wave equation is discussed. We also find as exact solution of soliton in the nonlinear wave equation analytically. We reveal that the velocity of the soliton is related to the second nearest neighbor interactions. We analytically evaluate the temporal evolution of the soliton and estimate the spectrum of the solitary wave using two dimensional FFT in case of different interactions. The result shows that the second nearest neighbor interactions affects the appearance of the lean of peak.
Published Version
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