XXI, 311 p. 116 illus., 84 illus. in color. online resource
This book presents a careful selection of the most important developments of the ɸ4 model, offering a judicious summary of this model with a view to future prospects and the challenges ahead. Over the past four decades, the ɸ4 model has been the basis for a broad array of developments in the physics and mathematics of nonlinear waves. From kinks to breathers, from continuum media to discrete lattices, from collisions of solitary waves to spectral properties, and from deterministic to stochastic models of ɸ4 (and ɸ6 ,ɸ8 ,ɸ12 variants more recently), this dynamical model has served as an excellent test bed for formulating and testing the ideas of nonlinear science and solitary waves.
Historical Perspectives of \phî4 Model -- Some Recent Developments on Kink Collisions -- Statistical Mechanics and Stochastic Aspects of \phî4 Models -- Discrete Variants of \phî4 Model -- Discrete Breathers in \phî4 and Related Models -- \phî4 Breathers: History and Recent Developments -- Decay of Bions in \phî4 Models -- \phî4 Model with a Potential -- \phî4 Model in Higher Dimensions -- Beyond the \phî4 Model: \phî6, \phî8, etc.
Mathematical Methods in Physics. http://scigraph.springernature.com/things/product-market-codes/P19013
Mathematical Applications in the Physical Sciences. http://scigraph.springernature.com/things/product-market-codes/M13120
Solid State Physics. http://scigraph.springernature.com/things/product-market-codes/P25013