THE INVARIANT MANIFOLDS FOR A PERTURBED
QUINTIC-CUBIC SCHR¨|ODINGER EQUATION 1

摘要/Abstract

摘要：

In this paper, the authors apply the analytical method to establish the per-
sistence of invariant manifolds for certain perturbation of the quintic-cubic Schr¨odinger
equation under even periodic boundary conditions.

中图分类号:

陈翰林, 郭柏林. THE INVARIANT MANIFOLDS FOR A PERTURBED
QUINTIC-CUBIC SCHR¨|ODINGER EQUATION 1[J]. 数学物理学报(英文版), 2004, 24(4): 536-548.

CHEN Han-Lin, GUO Bai-Lin. THE INVARIANT MANIFOLDS FOR A PERTURBED
QUINTIC-CUBIC SCHR¨|ODINGER EQUATION 1[J]. Acta mathematica scientia,Series B, 2004, 24(4): 536-548.

参考文献

[1] Li Y, Mclaughlin D W, Shatah J, Wiggins S. Persistent homoclinic orbits for a perturbed nonlinear
Schr¨odinger equation. Comm Pure and Appl Math, 1996, 49: 1175-1255

[2] Mclaughlin D W, Shatah J. Melnikov Analysis for Pde’s. Lectures in Appl Math, 1996, 31: 51-100

[3] Ball J M. Saddle point analysis for an ODE in a Banach space, and an application to dynamic bucking of
a beam. Nonlinear Elasticity, 1973. 93-160

[4] Bates P W, Lu K, Zong C. Persistence of overflowing manifolds for semiflow. Comm Pure Appl Math,
1999, 52: 983-1046

[5] Hale J. Ordinary Differential equations. New York: Robert E Krieger Publishing Co, 1980

[6] Guo Boling, Jing Zhujun, Lu Bainian. Slow timeperiodic solutions of cubic quintic Ginzburg-Landau
equation(I). Prog Nat Sci, 1998, 8(4): 403-415

[7] Mclaughlin D W, Overman E. Whiskered tori for integrable PDEs: chaotic behavior in near integrable
PDEs. Surveys in Appl Math, Vol 1. New York: Plenum, 1995. 83-203

[8] Guo Boling, Jing Zhujun, Lu Bainian. Spatotemporal complexity of the cubic Ginzburg-Landau equation.
Comm on Nonl Sci, and Num Simul, 1996, 2(2): 7-14

[9] Yagasaki K. The method of Melnikov for perturbations of multi-degree-of-freedom Hamiltonian systems.
Nonlinearity, 1999, 12: 799-822

[10] Kapitula T, Rubin J. Existence and stability of standing hole solutions to Complex Ginzburg-Landau
equations. Nonlinearity, 2000, 13: 77-112

[11] Kovacic G. Singular perturbation theory for homoclinic orbits in a class of near integrable dissipative
system. SIAM J Math Anal, 1995, 26: 1611-1643

[12] Fenichel N. Geometric singular perturbation theory for ordinary differential equations. J Differential
Equations, 1979, 31: 53-98

[13] Wiggins S. Global Bifurcations and Chaos, Analytic Methods. New York: Springer-Verlag, 1988

[14] Li Y, Wiggins S. Invariant manifolds and their fiberations for perturbed NLS equations. New York:
Spring-Verlag, 1997

[15] Cazenave T. An Introduction to Nonlinear Schr¨odinger Equations. IMUFRJ Rio De Janeiro, 1989. 22

[16] Chen Hanlin, Dai Zhengde. Exponential attrctor of the Cauchy Problem of disspative Zakharov equations
in R. Acta Math Sci, 2001, 20A(3): 373-383