Last Friday, Dr L.Debnath gave us a seminar on solitons which focus on the solution of the nonlinear system.

At first, Dr Debnath presented the history of the solitons and inverse scatter transfer with much detail. From 1834 to 1876, the solitary was studied initially and Lord Reyloigh profile the solitary but not formulate it. Later, He built a partial differential equation which was related mainly on two terms: evaluation term and nonlinear term. Using the concept of the unique balance, the solitary wave was first studied.For the strictly nonlinear phenomena, there are three cases which include no nonlinear term (no solitary wave) and solution case.

In 1955, the model methods were developed a lot. the nonlinear mass-spring model was studied. At this time, nonlinear recurrence phenomenon which is related with a series of the recurrence state were discovered and the continuous mass-spring system was studied more widely.

In 1965, Martin Krud and Norman Zabusky formulated a continuous equations which marked the great development of the research of of the solitary waves. Zabusky first called the waves as solitons.

The study of the solitons are so important for it can be arise from the following areas: fluid dynamics, solid mechanics, plasma physics, cordasal matter physics, nonlinear optics, etc.

Dr Debnath then presented the general model of the solitons, for example, the loguitudiual dispusive (?) waves in the elastic string (three degree partial differential equation in two dimensions.). To this model three special cases which include the nonlinear IVP problem were introduced.

He then introduced the two major difficults: superposition principle fails and integral transform (or Grean's function) can not be used.

At last, Dr Debnath show that in the two solitons interaction model, after interaction, the identity of solitons remain unchanged only when the phase changes occurs. He also introduce some references for the topic.

Last Update: 2/9/98
Web Author: Zizhong Wang
The report is for Dr Paprzycki@ marcin.paprzycki@ibspan.waw.pl or@ Home Page