摘要:

The initial value problem associated with the Benjamin‐Ono equation is linearized by a suitable extension of the inverse scattering transform. Essential is the formulation and solution of an associated nonlocal Riemann‐Hilbert problem in terms of initial scattering data. Solitons are given a definitive spectral characterization. Pure soliton solutions are obtained by solving a linear algebraic system whose coefficients depend linearly on [INLINEEQUATION], [INLINEEQUATI

ISSN:0022-2526    

DOI:10.1002/sapm19836811

年代:1983

数据来源: WILEY

摘要:

An invariant representation of the modulation equations for the sinh‐ and sine‐Gordon wavetrains is derived. A simple derivation of the representation which makes fundamental use of squared eigenfunctions is presented. This representation is used to place the modulation equations in Riemann invariant form and to cast them in a Hamiltonian form. The multiphase sinh‐Gordon study is complete, while the sine‐Gordon theory for more than one phase possesses technical difficulties which are described in the text. Explicit results on real two‐phase sine‐Gordon waves are included in

ISSN:0022-2526    

DOI:10.1002/sapm198368111

年代:1983

数据来源: WILEY

摘要:

This paper contains a description of a simple technique for analyzing a multivariable data set to detect significant clustering of data points. The method is illustrated by application to geographic leukemia and lymphoma incidence data in the Atlanta and Providence areas. Unusual clustering patterns are observed for myeloma cases when compared with those of other lymphomas.

ISSN:0022-2526    

DOI:10.1002/sapm198368161

年代:1983

数据来源: WILEY