Introduction to Soliton Theory: Applications to Mechanics

1. Front Matter

   Pages i-xi

   PDF

2. Introduction to Soliton Theory

   1. Mathematical Methods

      Pages 1-52

   2. Some Properties of Nonlinear Equations

      Pages 53-77

   3. Solitons and Nonlinear Equations

      Pages 78-120

3. Applications to Mechanics

   1. Statics and Dynamics of the Thin Elastic Rod

      Pages 121-148

   2. Vibrations of Thin Elastic Rods

      Pages 149-172

   3. The Coupled Pendulum

      Pages 173-196

   4. Dynamics of the Left Ventricle

      Pages 197-219

   5. The Flow of Blood in Arteries

      Pages 220-241

   6. Intermodal Interaction of Waves

      Pages 242-272

   7. On the Tzitzeica Surfaces and Some Related Problems

      Pages 273-297

4. Back Matter

   Pages 298-315

   PDF

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, Éd. 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.

• Cantor
• Oscillation
• Pendulum
• Vibration
• equation
• mechanics
• soliton
• statics

• Institute of Solid Mechanics, Romanian Academy, Bucharest, Romania

  Ligia Munteanu

• Department of Mathematics, Technical University of Civil Engineering, Bucharest, Romania

  Stefania Donescu

Policies and ethics