Existence of solitons in the nonlinear beam equation

被引：3

作者：

Benci, Vieri ^{[1
,2
]}

Fortunato, Donato ^{[3
]}

机构：

[1] Univ Pisa, Dipartimento Matemat Applicata U Dini, I-56127 Pisa, Italy

[2] King Saud Univ, Coll Sci, Dept Math, Riyadh 11451, Saudi Arabia

[3] Univ Bari Aldo Moro, Dipartimento Matemat, I-70125 Bari, Italy

来源：

JOURNAL OF FIXED POINT THEORY AND APPLICATIONS | 2012年 / 11卷 / 02期

关键词：

Nonlinear beam equation; travelling solitary waves; hylomorphic solitons; variational methods; OSCILLATIONS; WAVES;

D O I：

10.1007/s11784-012-0080-5

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper concerns the existence of solitons, namely stable solitary waves in the nonlinear beam equation with a suitable nonlinearity. An equation of this type has been introduced in [P. J. McKenna and W. Walter, Arch. Ration. Mech. Anal., 98 (1987), 167-177] as a model of a suspension bridge. We prove both the existence of solitary waves for a large class of nonlinearities and their stability. As far as we know this is the first result about stability of solitary waves in nonlinear beam equation.

引用

页码：261 / 278

页数：18

共 11 条

[1]

Bellazzini J, 2010, ADV NONLINEAR STUD, V10, P481

[2]

Bellazzini J, 2009, DYNAM PART DIFFER EQ, V6, P311

[3] Solitary waves in the nonlinear wave equation and in gauge theories [J].