摘要:

It is well known that the Kadomtsev‐Petviashvili (KP) equation is the two‐dimensional analogue of the Korteweg—de Vries (KdV) equation. We reconsider the derivation of the KP equation, modified to include the effects of rotation, in order to determine the nature of the initial conditions. The motivation for this is that if the solutions of the modified KP equation are assumed to be locally confined, then they satisfy a certain constraint, which appears to restrict considerably the class of allowed initial conditions. The outcome of the analysis presented here is that in general it is not permissible to assume that solutions of the modified KP equation are locally confined, and hence the constraint cannot be applied. The reason for this is the radiation of Poincaré waves, which appear behind the main part of the solution described by the modified KP eq

ISSN:0022-2526    

DOI:10.1002/sapm1989803183

年代:1989

数据来源: WILEY

摘要:

A model equation describing the configuration of a simple plasma maintained by external radiation is studied. A branch of steady solutions of the equation was found by Eckhaus et al. to terminate at a finite critical value of the power of the external source, and this is attributed to the discontinuous nature of a nonlinear term in the governing equation. On introducing a small parameter to render the term continuous, a second branch of solutions is constructed in a neighborhood of the termination point of the original branch. This suggests that the termination point is formed as the limit of a subcritical fold in the surface of the steady solution branch.

ISSN:0022-2526    

DOI:10.1002/sapm1989803203

年代:1989

数据来源: WILEY

摘要:

A class of multidimensional nonlinear evolution equations of physical interest are considered in the limit of strong coupling. It turns out that the initial value solution is readily obtained. In the special case of the Davey‐Stewartson equation the inverse scattering transform is shown to reduce to the obtained solution via perturbation. A number of other features are discussed as well, such as action angle variables, periodic solutions, and quantum analogue

ISSN:0022-2526    

DOI:10.1002/sapm1989803229

年代:1989

数据来源: WILEY

摘要:

We study the set of ordinary differential equations governing the homopolar disk dynamo. It is found that this set, which is a modification of the Lorenz system, has strange attractors of Lorenz type whenR(which corresponds to the Rayleigh number of the Lorenz system) tends to infinity. A central aspect of this study is that the Poincare map for this limit can be obtained through Melnikov's perturbation method, in contrast to the usual dependence on numerical computation.

ISSN:0022-2526    

DOI:10.1002/sapm1989803239

年代:1989

数据来源: WILEY

摘要:

The Korteweg—de Vries and nonlinear Schrödinger equations with an external forcing of distribution type are considered. The reflection coefficient is found to satisfy a nonlinear equation of a certain characteristic form which also appears in the semi‐infinite pro

ISSN:0022-2526    

DOI:10.1002/sapm1989803253

年代:1989

数据来源: WILEY