This paper presents analysis of the nonlinear interaction of a pair of solitary waves, the splitting of an isolated hump into a train of solitary waves, and the fission of a single solitary wave on reaching a shelf. Such interactions and splitting behaviour are usually described in the Korteweg–de Vries equation using the Hirota method, or more generally in terms of inverse scattering, a type o...

Mathematical modeling and algorithms of direct,and inverse electromagnetic scattering formulation due to biological tissues are investigated. The algorithms are used for a model based illustration technique within the microwave range. A number of methods is given to solve the direct,and inverse electromagnetic scattering problem in which the nonlinear and ill-posed nature of the problem are ack...