ISSN:0010-3640    

DOI:10.1002/cpa.3160440502

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

年代:1991

数据来源: WILEY

摘要:

AbstractWe study regiorously the solvability of the direct and inverse problems associated with Ψx–JΨy=QΨ,(x,y) ∈ ℝ2, where (i) Ψ is anN×N‐matrix‐valued function on ℝ2(N≦ 2), (ii)Jis a constant, real, diagonalN×Nmatrix with entries,J1>J2>…︁>JNand (iii)Qis off‐diagonal with rapidly decreasing (Schwartz) component functions. In particular we show that the direct problem is always solvable and give a small norm condition for the solvability of the inverse problem. In the particular case thatQis skew Hermitian the inverse problem is solvable without the small norm assumption. Furthermore we show how these results can be used to solve certain Cauchy problems for the associated nonlinear evolution equations. For concreteness we consider the N‐wave interactions and show that if a certain norm ofQ(x,y, 0) is smallor ifQ(x,y, 0) is skew Hermitian the N‐wave interations equation

ISSN:0010-3640    

DOI:10.1002/cpa.3160440503

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

年代:1991

数据来源: WILEY

ISSN:0010-3640    

DOI:10.1002/cpa.3160440504

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

年代:1991

数据来源: WILEY

ISSN:0010-3640    

DOI:10.1002/cpa.3160440501

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

年代:1991

数据来源: WILEY