Waves Called Solitons: Concepts and Experiments

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Review: While sounding like the latest episode from Power Rangers, this book is actually a translation of work done in the early 90's that shared it's place in the sun. The authors use Discrete Math arguements to link Hirato's equation to Pluckers equation on transformational evolution. This basic area links self organizational theory, deterministic chaos, cubic schrodeger and Kortig deVrie into a concept almost reminiscent of Hadamards work on odd order integers in cylindrical differential equations. (Dirac's sea of holes, with Fermions and Bosons linked via a Jungian archetype to the Beatles sea of holes in the Yellow Submarine.) Seriously though this area is almost untouched although brushed up against many times,(Stokes, Kortig,Bossinesq,etc.) The concept of self similarties on infintesimal differential equations producing evolution equations shows up in many forms(check Herman Haken's works). The reviewer first became aware when plotting in Mathcad or Matlab the Bessel Airy equations and the explicit form of the deep water equation. (both indentical) with similarites showing up in 1/3's. Called solitons or n-solitons the symmetries are amazing! At first the reviewer thought they were Moire Patterns due to aliasing, but after repeated math tests, confirmed the patterns. Spectral analysis, and wavelet analysis showed their self organized similarites explicitly,both in polynomial content and best basis. Check this out using Matlab's System Identification toolbox after converting the system to theta format. (this allows conversion to state systems and characteristic equations that are part of this story).