Introduction to Soliton Theory: Applications to Mechanics

ISBN-13: 9789048166848 / Angielski / Miękka / 2011 / 222 str.

Ligia Munteanu; Stefania Donescu

Opis

This monograph is planned to provide the application of the soliton theory to solve certain practical problems selected from the fields of solid mechanics, fluid mechanics and biomechanics. The work is based mainly on the authors' research carried out at their home institutes, and on some specified, significant results existing in the published literature. The methodology to study a given evolution equation is to seek the waves of permanent form, to test whether it possesses any symmetry properties, and whether it is stable and solitonic in nature. Students of physics, applied mathematics, and engineering are usually exposed to various branches of nonlinear mechanics, especially to the soliton theory. The soliton is regarded as an entity, a quasi-particle, which conserves its character and interacts with the surroundings and other solitons as a particle. It is related to a strange phenomenon, which consists in the propagation of certain waves without attenuation in dissipative media. This phenomenon has been known for about 200 years (it was described, for example, by the Joule Verne's novel Les histoires de Jean Marie Cabidoulin, Ed. Hetzel), but its detailed quantitative description became possible only in the last 30 years due to the exceptional development of computers. The discovery of the physical soliton is attributed to John Scott Russell. In 1834, Russell was observing a boat being drawn along a narrow channel by a pair of horses.

Spis treści

to Soliton Theory.- Mathematical Methods.- Some Properties of Nonlinear Equations.- Solitons and Nonlinear Equations.- Applications to Mechanics.- Statics and Dynamics of the Thin Elastic Rod.- Vibrations of Thin Elastic Rods.- The Coupled Pendulum.- Dynamics of the Left Ventricle.- The Flow of Blood in Arteries.- Intermodal Interaction of Waves.- On the Tzitzeica Surfaces and Some Related Problems.

Blurb

This monograph provides the application of soliton theory to solve certain problems selected from the fields of mechanics. The work is based of the authors’ research, and on some specified, significant results existing in the literature.

The present monograph is not a simple translation of its predecessor appeared in Publishing House of the Romanian Academy in 2002. Improvements outline the way in which the soliton theory is applied to solve some engineering problems. The book addresses concrete resolution methods of certain problems such as the motion of thin elastic rod, vibrations of initial deformed thin elastic rod, the coupled pendulum oscillations, dynamics of left ventricle, transient flow of blood in arteries, the subharmonic waves generation in a piezoelectric plate with Cantor-like structure, and some problems related to Tzitzeica surfaces.

This comprehensive study enables the readers to make connections between the soliton physical phenomenon and some partical, engineering problems.