Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

On the dissipative evolution equations associated with the Zakharov-Shabat system with a quadratic spectral parameter


Author: Jyh-Hao Lee
Journal: Trans. Amer. Math. Soc. 316 (1989), 327-336
MSC: Primary 35Q20; Secondary 34A55, 34B25
MathSciNet review: 943304
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we derive some results for the Zakharov-Shabat system of the form $ dm/dx = {z^2}[J,m] + (zQ + P)m$; $ J$ is diagonal and skew-Hermitian $ [8,10,12]$. Following the idea of R. Beals and R. R. Coifman, we estimate the wedge products of the columns of $ m$ by $ {L^2}$-norm of the potential $ (Q,P)\,[4]$. By this result we have the global existence of the dissipative evolution equations associated with this spectral problem if the generic initial data $ (Q(x,0),\,P(x,0)) = ({Q_0},{P_0})$ is of Schwartz class.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 35Q20, 34A55, 34B25

Retrieve articles in all journals with MSC: 35Q20, 34A55, 34B25


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1989-0943304-6
PII: S 0002-9947(1989)0943304-6
Keywords: Integrable evolution equations, inverse scattering transform, Zakharov-Shabat system
Article copyright: © Copyright 1989 American Mathematical Society