Variational methods in nonlinear field equations : solitary waves, hylomorphic solitons and vortices / Vieri Benci, Donato Fortunato.

Format:

Book

Author/Creator:

Benci, V. (Vieri), author.

Fortunato, D. (Donato), author.

Series:

Springer monographs in mathematics

Springer monographs in mathematics, 1439-7382

Language:

English

Subjects (All):

Differential equations, Nonlinear.

Nonlinear wave equations.

Variational inequalities (Mathematics).

Physical Description:

xvii, 250 pages ; 24 cm.

Place of Publication:

Cham : Springer, [2014]

Summary:

The book analyzes the existence of solitons, namely of finite energy solutions of field equations which exhibit stability properties. The book is divided in two parts. In the first part, the authors give an abstract definition of solitary wave and soliton and we develop an abstract existence theory for hylomorphic solitons, namely for those solitons which minimize the energy for a given charge. In the second part, the authors apply this theory to prove the existence of hylomorphic solitons for some classes of field equations (nonlinear Klein-Gordon-Maxwell equations, nonlinear Schrödinger-Maxwell equations, nonlinear beam equation,..). The abstract theory is sufficiently flexible to be applied to other situations, like the existence of vortices. The books is addressed to Mathematicians and Physicists.

Contents:

The general principles

Solitary waves and solitons: abstract theory

The nonlinear Schrödinger equation

The nonlinear Klein-Gordon equation

The Nonlinear Klein-Gordon-Maxwell equations

The nonlinear Schrödinger-Maxwell equations

The nonlinear beam equation

Vortices

Appendix.

Notes:

Includes bibliographical references (pages 245-250).

ISBN:

9783319069135

3319069136

OCLC:

881450047