摘要:

The form of weakly nonlinear waves of permanent form on deep water is considered under the effect of both surface tension and gravity. The Wilton ripple phenomenon is reexamined and shown to be associated with a bifurcation in which a wave of permanent form can double its period. It is shown further that Wilton's ripples are a special case of a more general phenomenon in which bifurcation into subharmonics and fractional higher harmonics can occur.

ISSN:0022-2526    

DOI:10.1002/sapm1979603183

年代:1979

数据来源: WILEY

摘要:

This paper analyzes the geometric structure of certain domains in the complex plane which arise in the asymptotic theory of linear ordinary differential equations containing a parameter. These domains, called admissible, are domains in which an asymptotic representation of the solution of the differential equation may be found and across whose boundaries these representations may undergo a rapid change of asymptotic behavior (the Stokes phenomenon). A knowledge of the disposition of those domains associated with a particular differential equation is necessary for a satisfactory asymptotic theory of the equation. The main analysis gives necessary and sufficient conditions for identifying admissible domains and gives a procedure for obtaining particular admissible subdomains of a given domain. Sufficient conditions are established to determine the maximality of admissible domains. A section of examples is included to highlight the salient features of this theory. In all of the results, criteria involving only purely local properties of the boundary are needed to determine the global properties of admissibility and maximal admissibility .

ISSN:0022-2526    

DOI:10.1002/sapm1979603211

年代:1979

数据来源: WILEY

摘要:

A method of asymptotically determining the bifurcating solutions of a nonlinear eigenvalue problem is described. The method is based on the smallness of a parameter which is different from the usual parameter used in the LyapunovSchmidt procedure. A discussion of the stability and evolution of bifurcating solutions is included. It is shown how the method may be useful for determining secondary bifurcations and turning points on bifurcation curves.

ISSN:0022-2526    

DOI:10.1002/sapm1979603241

年代:1979

数据来源: WILEY

摘要:

A first‐order theory for the development of a wind‐driven wave field is proposed. This takes advantage of the physical interpretation presented by Lake and Yuen (1978) that a nonlinear wind‐wave system can be completely characterized, to first approximation, by a single nonlinear wave train with carrier frequency coinciding with the local dominant frequency. The result is the nonlinear Schrodinger equation for the wave envelope, supplemented by an equation describing the change of dominant‐wave frequency (or wavenumber) with fetch (or duration). The latter equation is a consequence of a form‐drag model proposed by Deardorff (1967) for the input of wind energy into the dominant wave. The extension of the model to a random wave field is briefly

ISSN:0022-2526    

DOI:10.1002/sapm1979603261

年代:1979

数据来源: WILEY

摘要:

A simple proof of the following result of Baumert et al. is given. IfAandBare chosen independently according to a probability distribution defined on subsets of annelement set, then the probability thatAcontainsBis at least . It's shown to lead to a stronger conclusion, and to suggest definition of concepts of “partition number” and of “orthogonality of partitions into chains” as well as several conj

ISSN:0022-2526    

DOI:10.1002/sapm1979603271

年代:1979

数据来源: WILEY

ISSN:0022-2526    

DOI:10.1002/sapm1979603277

年代:1979

数据来源: WILEY

ISSN:0022-2526    

DOI:10.1002/sapm1979603286

年代:1979

数据来源: WILEY