On well-posedness of the third-order nonlinear Schrodinger equation with time-dependent coefficients

Author(s)

Carvajal, Xavier ^[1] ; Panthee, Mahendra ^[2] ; Scialom, Marcia ^[2]

Affiliation

^[1] Univ Fed Rio de Janeiro, Inst Matemat, BR-21941972 Rio de Janeiro, RJ - Brazil

^[2] Univ Estadual Campinas, IMECC, BR-13083859 Campinas, SP - Brazil

• Document type: Journal article
• Source: COMMUNICATIONS IN CONTEMPORARY MATHEMATICS; v. 17, n. 4 AUG 2015.
• Web of Science Citations: 0

Abstract

We consider the Cauchy problem associated to the third-order nonlinear Schrodinger equation with time-dependent coefficients. Depending on the nature of the coefficients, we prove local as well as global well-posedness results for given data in L-2-based Sobolev spaces. We also address the scaling limit to fast dispersion management and prove that it converges in H-1 to the solution of the averaged equation. (AU)

• FAPESP's process: 12/23054-6 - Properties of solutions of some dispersive equations
• Grantee: Marcia Assumpcao Guimaraes Scialom
• Support Opportunities: Research Grants - Visiting Researcher Grant - Brazil
• FAPESP's process: 12/20966-4 - Well-posedness of the Cauchy problem and stability theory for nonlinear dispersive equations
• Grantee: Mahendra Prasad Panthee
• Support Opportunities: Regular Research Grants