Several Kinds Of Nonlinear Evolution Equations And Solitary Wave Solutions And Shock Wave Solutions In Elastic Rod Waveguides

In 1960s the research upsurge of the nonlinear problems appeared simultaneously in many science branches in natural science. The research in many aspects formed nonlinear onrush. Many new physical phenomena such as soliton, turbulence, chaos, fractal and complex system etc. were discovered, which greatly expanded the people's view, and leaded to a great revolution in epistemology and development viewpoint in natural science. The nonlinear science has been an important symbol in the development of modern science. It is the actual fundamental study jointly concerned by various science branches in natural science. The nonlinear science involves lots of complex phenomena in nature, and has broad application prospect. Especially the researches in nonlinear dynamics and nonlinear wave-motion have extraordinary significance in solving problems and complicated phenomena encountered in physics, chemistry, biology and geophysics.The establishment of soliton theory is an important achievement in the development of nonlinear science. In many nonlinear physics fields, it has been found that large quantities of nonlinear evolution equations had soliton solutions. The common characteristic of these equations are that they have infinite conservation rules, and can be solved by inverse scattering method, and have Backlund transform, and can be completely integrated et al. The typical properties of soliton are that its propagation accompanies energy centralization and the interacting among solitons shows behaviors similar to...