Australian Mathematical Society (AustMS): E-Journals
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The second shifted difference of partitions and its applications
No full texthttp://dx.doi.org/10.1017/S000497271200033
Estimating the size of the (H, G)-coincidences set in representation spheres
No full texthttp://dx.doi.org/10.1017/S000497271200033
A note on M\"{o}bius disjointness for skew products on a circle and a nilmanifold
No full texthttp://dx.doi.org/10.1017/S000497271200033
On the fibres of an elliptic surface where rank does not jump
No full texthttp://dx.doi.org/10.1017/S000497272200136
Proof of a conjecture of Banerjee and Dastidar on odd crank
No full texthttp://dx.doi.org/10.1017/S000497271200033
Pilot-wave hydrodynamics: quantisation of partial integrability from a nonlinear integro-differential equation of the second order
No full texthttp://dx.doi.org/10.1017/S000497271200033
A modification to the Schrödinger equation for broader bandwidth gravity-capillary waves on deep water with depth-uniform current
No full textWe derive a nonlinear Schrödinger equation for the propagation of the three-dimensional broader bandwidth gravity-capillary waves including the effect of depth-uniform current. In this derivation, the restriction of narrow bandwidth constraint is extended, so that this equation will be more appropriate for application to a realistic sea wave spectrum. From this equation, an instability condition is obtained and then instability regions in the perturbed wavenumber space for a uniform wave train are drawn, which are in good agreement with the exact numerical results. As it turns out, the corrections to the stability properties that occur at the fourth-order term arise from an interaction between the mean flow and the frequency-dispersion term. Since the frequency-dispersion term, in the absence of depth-uniform current, for pure capillary waves is of opposite sign for pure gravity waves, so too are the corrections to the instability properties.
doi: 10.1017/S144618112300002