摘要:

The inverse scattering problem for cubic eigenvalue equations of the formψxxx+ 6Qψx+ 6Rψ= λψis outlined and formally solved. Many properties of the scattering data are obtained, the continuous spectrum is briefly discussed, special one soliton solutions are obtained, and the infinity of conserved quantities are determined in terms of the scattering

ISSN:0022-2526    

DOI:10.1002/sapm1980623189

年代:1980

数据来源: WILEY

摘要:

This paper is concerned with a nonlinear integrodifferential equation (the delay logistic equation) governing the growth dynamics of a single speciesN(t) for timet>0. This equation contains a positive parameter λ. Suppose that there exists a positive equilibrium solutionN=cwhich is stable for all small values of λ. Assume also that this solution loses stability as λ is increased past a critical value λ*. This will correspond to a simple pure imaginary conjugate pair of roots of a characteristic equation associated with the linearized stability ofN=cat λ = λ*. Then we will construct a unique bifurcating time periodic solution of the equation as a Taylor series in a parameter ε. Furthermore this solution exists either for supercritical values of the parameter (λ>λ*) or for subcritical values (λ<λ*). The stability behavior of this small periodic solution can be characterized according to whether the bifurcation is supercritical or subcritical‐supercritical solutions are stable, but subcritical solutions are unstable. Therefore these results are analogous to Hoprs bifurcation theorem for autonomous systems of differenti

ISSN:0022-2526    

DOI:10.1002/sapm1980623217

年代:1980

数据来源: WILEY

摘要:

An equation is derived that governs the evolution in two spatial dimensions of long internal waves in fluids of great depth. The equation is a natural generalization of Benjamin's (1967) one‐dimensional equation, and relates to it in the same way that the equation of Kadomtsev and Petviashvili relates to the Kortewegde‐Vries equation. The stability of one‐dimensional solitons with respect to long transverse disturbances is studied in the context of this equation. Solitons are found to be unstable with respect to such perturbations in any system in which the phase speed is a minimum (rather than a maximum) for the longest waves. Internal waves do not have this property, and are not unstable with respect to such perturba

ISSN:0022-2526    

DOI:10.1002/sapm1980623249

年代:1980

数据来源: WILEY

摘要:

This paper concerns the equilibrium structure of Maclaurin spheroids and Jacobi ellipsoids embedded in nonrotating halos of uniform density. The halo is assumed unresponsive to the embedded object, whereas the embedded object is allowed to respond to the gravitational field of the halo. We also ignore the effects of the halo pressure field on the embedded object. It is shown how the halo modifies the classical Maclaurin and Jacobi sequences. In particular, we locate the intersection of these two sequences, i.e., the point of bifurcation, and present a formula for the eccentricity at bifurcation (eb) as a function of the ratio of halo density to density of rotating matter (ρH/ρB). We find that the halo increases the eccentricity at bifurcation; thus, it has a stabilizing influence. However, secular instability is never entirely suppressed, sinceeb→1 only forρH/ρB→∞. It is seen that the Ostrike‐Peebles conjecture does not apply to the cas

ISSN:0022-2526    

DOI:10.1002/sapm1980623263

年代:1980

数据来源: WILEY

摘要:

The concept of a doubly stochastic matrix whose entries come from a convex subset of the unit square is defined. It is proved that the only convex subsets of the unit square which contain (0,0) and (1, 1) and allow an extension of Birkhoff's characterization of the extreme points of the set of doubly stochastic matrices are parallelograms. A sufficient condition is given for a matrix to be extreme when the convex subset is not a parallelogram.

ISSN:0022-2526    

DOI:10.1002/sapm1980623273

年代:1980

数据来源: WILEY

ISSN:0022-2526    

DOI:10.1002/sapm1980623281

年代:1980

数据来源: WILEY