摘要:

A previously derived equation and boundary condition [the generalized Kadomtsev‐Petviashvili system] is used to describe the propagation of stable solitary waves in open seas and marine straits. The GKP system is transformed, under specific geophysical conditions, into a simpler system that allows exact soliton type solutions. The curved wave crests corresponding to these solutions are plotted for several choices of the depth function and side boundarie

ISSN:0022-2526    

DOI:10.1002/sapm19898011

年代:1989

数据来源: WILEY

摘要:

This paper describes several combinatorial models for Laguerre, Charlier, and Hermite polynomials, and uses them to prove combinatorially some classical formulas. The so‐called “Italian limit formula” (from Laguerre to Hermite), the Appel identity for Hermite polynomials, and the two Sheffer identities for Laguerre and Charlier polynomials are proved. We also give bijective proofs of the three‐term recurrences. These three families form the bottom triangle in R. Askey's chart classifying hypergeometric orthogonal poly

ISSN:0022-2526    

DOI:10.1002/sapm198980125

年代:1989

数据来源: WILEY

摘要:

A general theory is presented for nonlinear instabilities arising in steady hydrodynamic motions. For quasiparallel flows at high values of the Reynolds number it is found that for relatively small disturbance levels the usual ideas concerning the generation of higher harmonics and the subsequent modification of the fundamental may be overwhelmed by three dimensional interactions between the evolving mean flow and the first harmonic wave. The differences from and similarities to existing asymptotic and numerical studies are discussed. The theory developed applies to a variety of flow configurations. Numerical results are given for Poiseuille flow and the Blasius boundary layer. In addition the theory developed here is applied to simulate the instabilities produced in a boundary layer due to the presence of free stream disturbances.

ISSN:0022-2526    

DOI:10.1002/sapm198980137

年代:1989

数据来源: WILEY

摘要:

The gravitational clustering of a multicomponent medium in an expanding universe has been considered by many authors in recent years. The system of differential equations associated with such a multicomponent medium is generalized in this article by incorporating arbitrary parameters. Explicit analytic solutions of this generalized system are given for various situations. Physical interpretations of the solutions are not considered, but the various solutions of physical problems obtained by various authors can be seen to be special cases of the general solutions given in this article.

ISSN:0022-2526    

DOI:10.1002/sapm198980175

年代:1989

数据来源: WILEY