Hylomorphic solitons

被引:16
作者
Benci, Vieri [1 ]
机构
[1] Univ Pisa, Dipartimento Matemat Applicata U Dini, I-56127 Pisa, Italy
关键词
Soliton; solitary waves; Q-ball; variational methods; nonlinear Schrodinger equation; nonlinear wave equation; nonlinear Klein-Gordon equation; KLEIN-GORDON-MAXWELL; SOLITARY WAVES; ASYMPTOTIC STABILITY; NONLINEAR-WAVE; STANDING WAVES; EXISTENCE; EQUATION; NONEXISTENCE;
D O I
10.1007/s00032-009-0105-8
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
This paper is devoted to the study of solitary waves and solitons whose existence is related to the ratio energy/charge. These solitary waves are called hylomorphic. This class includes the Q-balls, which are spherically symmetric solutions of the nonlinear Klein-Gordon equation, as well as solitary waves and vortices which occur, by the same mechanism, in the nonlinear Schrodinger equation and in gauge theories. Mainly we will be interested in the very general principles which are at the base of the existence of solitons such as the Variational Principle, the Invariance Principle, the Noether's theorem, the Hamilton-Jacobi theory etc. We give a general definition of hylomorphic solitons and an interpretation of their nature (swarm interpretation) which is very helpful in understanding their behavior. We apply these ideas to the Nonlinear Schrodinger Equation and to the Nonlinear Klein-Gordon Equation respectively.
引用
收藏
页码:271 / 332
页数:62
相关论文
共 39 条
[1]  
Badiale M, 2007, J EUR MATH SOC, V9, P355
[2]  
Bellazzini J, 2007, ADV NONLINEAR STUD, V7, P439
[3]  
BELLAZZINI J, ARXIV07121103
[4]  
BELLAZZINI J, ARXIV08105079
[5]  
BELLAZZINI J, NONLINEAR SCHRODINGE
[6]   Soliton like solutions of a Lorentz invariant equation in dimension 3 [J].
Benci, V ;
Fortunato, D ;
Pisani, L .
REVIEWS IN MATHEMATICAL PHYSICS, 1998, 10 (03) :315-344
[7]  
Benci V, 2003, ADV NONLINEAR STUD, V3, P151
[8]  
Benci V, 2004, NONLINEAR ANALYSIS AND APPLICATIONS TO PHYSICAL SCIENCES, P1
[9]   Solitary waves of the nonlinear Klein-Gordon equation coupled with the Maxwell equations [J].
Benci, V ;
Fortunato, D .
REVIEWS IN MATHEMATICAL PHYSICS, 2002, 14 (04) :409-420
[10]  
BENCI V, 2008, NONLINEAR ANAL TMA