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Chapter1 Introduction; References; Chapter2 Acoustic Solitons; 2.1 Fermi-Pasta-Ulam Problem (FPU); 2.2 Solitary Waves; 2.3 Solitons in the Toda Chain; 2.4 Numerical Methods for Finding Soliton Solution; 2.5 Solitons in the Lennard-Jones Chain; 2.6 Solitons in the Diatomic Chain; 2.6.1 Model of the Diatomic Chain; 2.6.2 Continuum Approximation; 2.6.3 Numerical Simulation of Soliton Dynamics; 2.7 Acoustic Solitons in a Helix Chain; 2.7.1 Model of a Helix Chain; 2.7.2 Dispersion Equation; 2.7.3 Numerical Methods for Finding the Soliton Solution; 2.7.4 Results of Numerical Analysis.
2.7.5 Soliton Interaction2.7.6 Modeling Acoustic Soliton Formation; 2.7.7 Interaction of Solitons with MolecularChain Heterogeneities; 2.8 Conclusion; References; Chapter3 Topological Solitons; 3.1 Solitons in a Chain with Substrate; 3.1.1 Stationary State of Topological Soliton; 3.1.2 Interaction of Topological Solitons; 3.1.3 Soliton Dynamics; 3.1.4 Supersonic Regimes of Topological Soliton Motion; 3.2 Solitons in an Anharmonic Chain; 3.2.1 Stationary Soliton State; 3.2.2 Vibrational Eigenmodes of a Topological Soliton; 3.2.3 Numerical Method for Findingthe Vibrational Eigenmodes.
3.3.3 Dispersion of Low-Amplitude Waves3.3.4 Stationary States of Topological Solitons; 3.3.5 Topological Soliton Dynamics; 3.3.6 Interaction of Topological Solitons; 3.3.7 Formation of Topological Solitonsin a Thermalized Lattice; 3.3.8 Conclusion; References; Chapter4 Localized Nonlinear Vibrations; 4.1 A Nonlinear Oscillator; 4.2 A Chain of Nonlinear Oscillators; 4.3 Numerical Method for Finding Breathers; 4.4 Properties of Discrete Breathers; References; Chapter5 Ratchets; 5.1 Asymmetric Pendulum; 5.1.1 Potential Function of an Asymmetric Pendulum; 5.1.2 Dynamical Equation.
5.1.3 Asymmetry of Chaotic Oscillations5.1.4 Asymmetric Particle Drift Velocity; 5.1.5 Frequency Dependence of the Drift Velocity; 5.1.6 Temperature Dependence of the Drift Velocity; 5.1.7 Amplitude Dependence of the Drift Velocity; 5.1.8 Isotope Dependence of the Particle Drift Velocity; 5.1.9 Conclusion; 5.2 Ratchet Dynamics of Solitons in the FK Model; 5.2.1 Asymmetric Chain Model; 5.2.2 Soliton Stationary State; 5.2.3 Soliton Dynamics; 5.2.4 Soliton Mobility; 5.2.5 Soliton Motion Induced by Low-Frequency Noise; 5.2.6 Conclusion.
2.7.5 Soliton Interaction2.7.6 Modeling Acoustic Soliton Formation; 2.7.7 Interaction of Solitons with MolecularChain Heterogeneities; 2.8 Conclusion; References; Chapter3 Topological Solitons; 3.1 Solitons in a Chain with Substrate; 3.1.1 Stationary State of Topological Soliton; 3.1.2 Interaction of Topological Solitons; 3.1.3 Soliton Dynamics; 3.1.4 Supersonic Regimes of Topological Soliton Motion; 3.2 Solitons in an Anharmonic Chain; 3.2.1 Stationary Soliton State; 3.2.2 Vibrational Eigenmodes of a Topological Soliton; 3.2.3 Numerical Method for Findingthe Vibrational Eigenmodes.
3.3.3 Dispersion of Low-Amplitude Waves3.3.4 Stationary States of Topological Solitons; 3.3.5 Topological Soliton Dynamics; 3.3.6 Interaction of Topological Solitons; 3.3.7 Formation of Topological Solitonsin a Thermalized Lattice; 3.3.8 Conclusion; References; Chapter4 Localized Nonlinear Vibrations; 4.1 A Nonlinear Oscillator; 4.2 A Chain of Nonlinear Oscillators; 4.3 Numerical Method for Finding Breathers; 4.4 Properties of Discrete Breathers; References; Chapter5 Ratchets; 5.1 Asymmetric Pendulum; 5.1.1 Potential Function of an Asymmetric Pendulum; 5.1.2 Dynamical Equation.
5.1.3 Asymmetry of Chaotic Oscillations5.1.4 Asymmetric Particle Drift Velocity; 5.1.5 Frequency Dependence of the Drift Velocity; 5.1.6 Temperature Dependence of the Drift Velocity; 5.1.7 Amplitude Dependence of the Drift Velocity; 5.1.8 Isotope Dependence of the Particle Drift Velocity; 5.1.9 Conclusion; 5.2 Ratchet Dynamics of Solitons in the FK Model; 5.2.1 Asymmetric Chain Model; 5.2.2 Soliton Stationary State; 5.2.3 Soliton Dynamics; 5.2.4 Soliton Mobility; 5.2.5 Soliton Motion Induced by Low-Frequency Noise; 5.2.6 Conclusion.