DSpace Collection:
https://dspace.lboro.ac.uk/2134/91
2015-07-04T15:30:22ZJordan-Kronecker invariants of finite-dimensional Lie algebras
https://dspace.lboro.ac.uk/2134/17892
Title: Jordan-Kronecker invariants of finite-dimensional Lie algebras
Authors: Bolsinov, Alexey V.; Zhang, Pumei
Abstract: For any finite-dimensional Lie algebra we introduce the notion of Jordan-Kronecker invariants, study their properties and discuss examples. These invariants naturally appear in the framework of the bi-Hamiltonian approach to integrable systems on Lie algebras and are closely related to Mischenko-Fomenko's argument shift method.2012-01-01T00:00:00ZNonlinear free surface flows past a semi-infinite flat plate in water of finite depth
https://dspace.lboro.ac.uk/2134/2969
Title: Nonlinear free surface flows past a semi-infinite flat plate in water of finite depth
Authors: Maleewong, M.; Grimshaw, Roger H.J.
Abstract: We consider the steady free surface two-dimensional flow past a semi-infinite flat plate in
water of a constant finite depth. The fluid is assumed to be inviscid, incompressible and
the flow is irrotational; surface tension at the free surface is neglected. Our concern is with
the periodic waves generated downstream of the plate edge. These can be characterized
by a depth-based Froude number, F, and the depth d (draft) of the depressed plate.
For small d and subcritical flows, we may use the linearized problem, combined with
conservation of momentum, to obtain some analytical results. These linear results are
valid when F is not close to 0 or 1. As F approaches 1, we use a weakly nonlinear longwave
analysis, and in particular show that the results can be extended to supercritical
flows. For larger d nonlinear effects need to be taken account, and so we solve the fully
nonlinear problem numerically using a boundary integral equation method. Here the
predicted wavelength from the linear and weakly nonlinear results is used to set the
mean depth condition for the nonlinear problem. The results by these three approaches
are in good agreement when d is relatively small. For larger d our numerical results are
compared with known results for the highest wave.We also find some wave-free solutions,
which when compared with the weakly nonlinear results are essentially just one-half of
a solitary wave solution.
Description: This is a pre-print.2007-01-01T00:00:00ZStationary Solutions of SPDEs and Infinite Horizon BDSDEs
https://dspace.lboro.ac.uk/2134/2895
Title: Stationary Solutions of SPDEs and Infinite Horizon BDSDEs
Authors: Zhang, Qi; Zhao, Huaizhong
Abstract: In this paper we study the existence of stationary solutions for stochastic partial differential
equations.
Description: This is a pre-print.2007-01-01T00:00:00ZThe theory of optical dispersive shock waves in photorefractive media
https://dspace.lboro.ac.uk/2134/2894
Title: The theory of optical dispersive shock waves in photorefractive media
Authors: El, G.A.; Gammal, A.; Khamis, E.G.; Kraenkel, R.A.; Kamchatnov, A.M.
Abstract: The theory of optical dispersive shocks generated in propagation of light beams through photore-
fractive media is developed. Full one-dimensional analytical theory based on the Whitham modu-
lation approach is given for the simplest case of sharp step-like initial discontinuity in a beam with
one-dimensional strip-like geometry. This approach is con¯rmed by numerical simulations which are
extended also to beams with cylindrical symmetry. The theory explains recent experiments where
such dispersive shock waves have been observed.
Description: This is a pre-print.2007-01-01T00:00:00Z