Existence of standing waves for the complex Ginzburg-Landau equation

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:422

Article

Cipolatti, Rolci¹  Dickstein, Flavio¹  Puel, Jean-Pierre² 

[1] Univ Fed Rio de Janeiro, Inst Matemat, BR-21944970 Rio De Janeiro, RJ, Brazil

[2] Univ Versailles St Quentin, CNRS, LMV, UMR 8100, F-78035 Versailles, France

关键词: Standing waves;    Complex Ginzburg-Landau equation;   

DOI  :  10.1016/j.jmaa.2014.08.057

来源: Elsevier

【 摘 要 】

We study the existence of standing wave solutions of the complex Ginzburg-Landau equation phi(t) - e(i0)(rho I - Delta)phi - e(i gamma)vertical bar phi vertical bar(alpha)phi = 0 in RN, where a > 0, (N - 2)alpha < 4, p > 0 and theta,gamma is an element of R. We show that for any is an element of (-pi/2, pi/2) there exists is an element of > 0 such that (GL) has a non-trivial standing wave solution if vertical bar gamma -theta vertical bar < is an element of. Analogous result is obtained in a ball Omega is an element of R-N for rho > -lambda(i), where lambda(1) is the first eigenvalue of the Laplace operator with Dirichlet boundary conditions. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

Free