Solitons and Compactons

Ji-Huan He, Donghua University
Shun-Dong Zhu

Abstract

Article Outline Glossary Definition of the Subject Introduction Solitons Compactons Generalized Solitons and Compacton-like Solutions Future Directions Cross References Bibliography Glossary Soliton A soliton is a stable pulse-like wave that can exist in some nonlinear systems. The soliton, after a collision with another soliton, eventually emerges unscathed. Compacton A compacton is a special solitary traveling wave that, unlike a soliton, does not have exponential tails. Generalized soliton A generalized soliton is a soliton with some free parameters. Generally a generalized soliton can be expressed by exponential functions. 8458 S Solitons and Compactons Compacton-like solution A compcton-like solution is a special wave solution which can be expressed by the squares of sinusoidal or cosinoidal functions. Definition of the Subject Soliton and compacton are two kinds of nonlinear waves. They play an indispensable and vital role in all ramifications of science and technology, and are used as constructive elements to formulate the complex dynamical behavior of wave systems throughout science: from hydrodynamics to nonlinear optics, from plasmas to shock waves, from tornados to theGreat Red Spot of Jupiter, from traffic flow to Internet, from Tsunamis to turbulence. More recently, soliton and compacton are of key importance in the quantum fields and nanotechnology especially in nanohydrodynamics.