On the susceptibility of bright nonlinear Schrodinger solitons to long-wave transverse instability

被引:4
作者
Bridges, TJ [1 ]
机构
[1] Univ Surrey, Dept Math & Stat, Guildford GU2 7XH, Surrey, England
来源
PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES | 2004年 / 460卷 / 2049期
关键词
solitary waves; optical media; transverse instability; multi-symplectic; nonlinear Schrodinger equation; Hamiltonian;
D O I
10.1098/rspa.2004.1330
中图分类号
O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];
学科分类号
07 ; 0710 ; 09 ;
摘要
A new theory for transverse instability of bright solitons of equations of nonlinear Schrodinger (NLS) type is presented, based on a natural deformation of the solitons into a four-parameter family. This deformation induces a set of four diagnostic functionals which encode information about transverse instability. These functionals include the deformed power, the deformed momentum and two new functionals. The main result is that a sufficient condition for long-wave transverse instability is completely determined by these functionals. Whereas longitudinal instability is determined by a single partial derivative (the Vakhitov-Kolokolov criterion), the condition for transverse instability requires 10 partial derivatives. The theory is illustrated by application to scalar NLS equations with general potential, and vector NLS equations for optical media with chi((2)) nonlinearity.
引用
收藏
页码:2605 / 2615
页数:11
相关论文
共 15 条
[1]   Two-dimensional solitary-waves in media with quadratic and cubic nonlinearity [J].
Bang, O ;
Kivshar, YS ;
Buryak, AV ;
De Rossi, A ;
Trillo, S .
PHYSICAL REVIEW E, 1998, 58 (04) :5057-5069
[3]  
Bridges TJ, 2001, ARCH RATION MECH AN, V156, P1, DOI 10.1007/s002050100123
[4]   Universal geometric condition for the transverse instability of solitary waves [J].
Bridges, TJ .
PHYSICAL REVIEW LETTERS, 2000, 84 (12) :2614-2617
[5]   Two-dimensional effects in nonlinear Kronig-Penney models [J].
Gaididei, YB ;
Christiansen, PL ;
Rasmussen, KO ;
Johansson, M .
PHYSICAL REVIEW B, 1997, 55 (20) :13365-13368
[6]   STABILITY THEORY OF SOLITARY WAVES IN THE PRESENCE OF SYMMETRY .1. [J].
GRILLAKIS, M ;
SHATAH, J ;
STRAUSS, W .
JOURNAL OF FUNCTIONAL ANALYSIS, 1987, 74 (01) :160-197
[7]   Self-focusing and transverse instabilities of solitary waves [J].
Kivshar, YS ;
Pelinovsky, DE .
PHYSICS REPORTS-REVIEW SECTION OF PHYSICS LETTERS, 2000, 331 (04) :118-195
[8]   SOLITON STABILITY IN PLASMAS AND HYDRODYNAMICS [J].
KUZNETSOV, EA ;
RUBENCHIK, AM ;
ZAKHAROV, VE .
PHYSICS REPORTS-REVIEW SECTION OF PHYSICS LETTERS, 1986, 142 (03) :103-165
[9]   Transverse instability of optical spatiotemporal solitons in quadratic media [J].
Liu, X ;
Beckwitt, K ;
Wise, F .
PHYSICAL REVIEW LETTERS, 2000, 85 (09) :1871-1874
[10]   Exact representations for coupled bright and dark solitary waves of quadratically nonlinear systems [J].
Parker, DF .
JOURNAL OF THE OPTICAL SOCIETY OF AMERICA B-OPTICAL PHYSICS, 1998, 15 (03) :1061-1068