Introduction -- PrefaceNonlinearity in classical mechanics -- A pendulum -- Vibration by a nonlinear spring force -- A jumping rope -- Hyperbolic and elliptic functions -- Variation principle -- Buckling deformation of a rodWave propagation, singularities and boundaries -- Elastic waves along a linear string of infinite length -- Microwave transmission -- Schr?odinger's equation -- Scattering by the potential V(x) = V b0 s sech p2 s x -- Two-dimensional waves in inhomogeneous medium -- Sound propagation in airSolitons and adiabatic potentials -- The Korteweg-deVries equation -- Steady solutions of the Korteweg-deVries equation -- Developing equations of nonlinear vector waves -- Bargmann's theorem -- Riccati's theorem -- Properties of the Eckart potential in the soliton field -- Zabusky-Kruskal's computational analysisStructural phase transitions -- Initial uncertainties and transition anomalies -- Dynamical theory of collective motion -- Pseudopotential and sine-Gordon equationNonlinear waves -- Elemental waves -- Matrix formulation for nonlinear development -- Heat dissipation of wave motion -- Born-Huang transitions in crystals -- Symmetry of media for the Korteweg-deVries equation -- Soliton descriptionScattering theory -- One-component waves -- Two-component scatteringsMethod of inverse scatterings -- Coherent wave packets and Marchenko's equation -- Reflectionless multi-soliton potentials -- Two-component systemsQuasi-static soliton states -- Developing the Korteweg-deVries equation -- Multi-soliton potentials in unsteady states -- The modified Korteweg-deVries equation, part 2 -- Thermodynamic instability and Breezer potentials -- The third-order Schr?odinger equationThe B?acklund transformation and sine-Gordon equations -- The Klein-Gordon equation -- The B?acklund transformation -- The sine-Gordon equation -- Numerical analysis of the sine-Gordon equation -- Inverse scatterings and the B?acklund transformation -- Scatterings by a pseudopotentialMiscellaneous applications -- Surface waves -- Vortex motion in fluid media -- Plasma oscillation -- Laser light transmission through absorbing media -- Periodic lattices.