Focusing singularity of the cubic Schrödinger equation

D. W. McLaughlin; G. C. Papanicolaou; C. Sulem; P. L. Sulem

doi:10.1103/PhysRevA.34.1200

Focusing singularity of the cubic Schrödinger equation

D. W. McLaughlin, G. C. Papanicolaou, C. Sulem, and P. L. Sulem

Phys. Rev. A 34, 1200 – Published 1 August 1986

Abstract

The cubic Schrödinger equation has singular solutions in two or more space dimensions. The singularities occur at points of intense self-focusing. In this paper we present numerical results that describe the nature of the focusing singularity.

Received 3 September 1985

DOI:https://doi.org/10.1103/PhysRevA.34.1200

Authors & Affiliations

D. W. McLaughlin

Department of Mathematics, University of Arizona, Tucson, Arizona 85721

G. C. Papanicolaou

Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, New York 10012

C. Sulem

Department of Mathematics, Ben Gurion University, Beer Sheva, Israel and Centre Mathematique Apliqueés, Centre National de la Recherche Scientifique, Ecole Normale Supérieure, Université de Paris VII, 75251 Paris Cédex, France

P. L. Sulem

School of Mathematical Sciences, Tel Aviv University, Tel Aviv, Israel and Observatoire de Nice, Centre National de la Recherche Scientifique, Université de Nice, Bote Postale 139, 06003 Nice Cédex, France

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Vol. 34, Iss. 2 — August 1986

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