Exploding dissipative solitons: The analog of the Ruelle-Takens route for spatially localized solutions

被引：42

作者：

Descalzi, Orazio ^{[1
,2
]}

Cartes, Carlos ^{[1
]}

Cisternas, Jaime ^{[1
]}

Brand, Helmut R. ^{[2
]}

机构：

[1] Univ Los Andes, Fac Ingn & Ciencias Aplicadas, Complex Syst Grp, Santiago, Chile

[2] Univ Bayreuth, Dept Phys, D-95440 Bayreuth, Germany

来源：

PHYSICAL REVIEW E | 2011年 / 83卷 / 05期

关键词：

PULSES;

D O I：

10.1103/PhysRevE.83.056214

中图分类号：

O35 [流体力学]; O53 [等离子体物理学];

学科分类号：

070204 ; 080103 ; 080704 ;

摘要：

We investigate the route to exploding dissipative solitons in the complex cubic-quintic Ginzburg-Landau equation, as the bifurcation parameter, the distance from linear onset, is increased. We find for a large class of initial conditions the sequence: stationary localized solutions, oscillatory localized solutions with one frequency, oscillatory localized solutions with two frequencies, and exploding localized solutions. The transition between localized solutions with one and with two frequencies, respectively, is analyzed in detail. It is found to correspond to a forward Hopf bifurcation for these localized solutions as the bifurcation parameter is increased. In addition, we make use of power spectra to characterize all time-dependent states. On the basis of all information available, we conclude that the sequence oscillatory localized solutions with one frequency, oscillatory localized solutions with two frequencies, and exploding dissipative solitons can be interpreted as the analog of the Ruelle-TakensNewhouse route to chaos for spatially localized solutions.

引用

页数：6

共 27 条

[1] Pulsating solitons, chaotic solitons, period doubling, and pulse coexistence in mode-locked lasers: Complex Ginzburg-Landau equation approach [J].

Akhmediev, N ;

Soto-Crespo, JM ;

Town, G .

PHYSICAL REVIEW E, 2001, 63 (05) :566021-566021

[2]

Akhmediev N, 2004, PHYS REV E, V70, DOI 10.1103/PhysRevE.70.036613

[3] Exploding solitons and Shil'nikov's theorem [J].

Akhmediev, N ;

Soto-Crespo, JM .

PHYSICS LETTERS A, 2003, 317 (3-4) :287-292

[4] INTERACTION OF LOCALIZED SOLUTIONS FOR SUBCRITICAL BIFURCATIONS [J].

BRAND, HR ;

DEISSLER, RJ .

PHYSICAL REVIEW LETTERS, 1989, 63 (26) :2801-2804

[5] PATTERN-FORMATION OUTSIDE OF EQUILIBRIUM [J].

CROSS, MC ;

HOHENBERG, PC .

REVIEWS OF MODERN PHYSICS, 1993, 65 (03) :851-1112

[6] Experimental evidence for soliton explosions [J].

Cundiff, ST ;

Soto-Crespo, JM ;

Akhmediev, N .

PHYSICAL REVIEW LETTERS, 2002, 88 (07) :739031-739034

[7] Effect of nonlinear gradient terms on breathing localized solutions in the quintic complex Ginzburg-Landau equation [J].

Deissler, RJ ;

Brand, HR .

PHYSICAL REVIEW LETTERS, 1998, 81 (18) :3856-3859

[8] PERIODIC, QUASI-PERIODIC, AND CHAOTIC LOCALIZED SOLUTIONS OF THE QUINTIC COMPLEX GINZBURG-LANDAU EQUATION [J].

DEISSLER, RJ ;

BRAND, HR .

PHYSICAL REVIEW LETTERS, 1994, 72 (04) :478-481

[9] Stable stationary and breathing holes at the onset of a weakly inverted instability [J].

Descalzi, O ;

Brand, HR .

PHYSICAL REVIEW E, 2005, 72 (05)

[10] Saddle-node bifurcation: Appearance mechanism of pulses in the subcritical complex Ginzburg-Landau equation [J].

Descalzi, O ;

Argentina, M ;

Tirapegui, E .

PHYSICAL REVIEW E, 2003, 67 (01) :4

← 1 2 3 →