摘要:

AbstractWe attack the multiphase averaged systems for the zero dispersion limit of the KdV equation. Attention is paid to the most important case—the single phase oscillations. A scheme is developed to solve the Whitham averaged system (single phase averaged system). This system, under our scheme, is transformed to a linear over‐determined system of Euler‐Poisson‐Darboux type whose solution can be written down explicitly. We show that, for any smooth initial data which has only one hump or is a nontrivial monotone function, the weak limit has single‐phase oscillations within a cusp in thex‐tplane for a short time after the breaking time for the corresponding Burgers equation. Outside the cusp, the limit satisfies the Burgers equation. More surprisingly, we also show that the weak limit has global single‐phase oscillations within a cusp for any smooth nontrivial monotone initial data with only one inflection point. © 1993 John W

ISSN:0010-3640    

DOI:10.1002/cpa.3160460802

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1993

数据来源: WILEY

ISSN:0010-3640    

DOI:10.1002/cpa.3160460803

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1993

数据来源: WILEY

ISSN:0010-3640    

DOI:10.1002/cpa.3160460801

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1993

数据来源: WILEY