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- JERRY L. BONA, S. M. SUN
- 2001

The Korteweg-de Vries equation was first derived by Boussinesq and Korteweg and de Vries as a model for long-crested small-amplitude long waves propagating on the surface of water. The same partial differential equation has since arisen as a model for unidirectional propagation of waves in a variety of physical systems. In mathematical studies,… (More)

Attention is given to the initial-boundary-value problems (IBVPs) u t + u x + uu x + u xxx = 0, for x, t ≥ 0, u(x, 0) = φ(x), u(0, t) = h(t) (0.1) for the Korteweg-de Vries (KdV) equation and u t + u x + uu x − u xx + u xxx = 0, for x, t ≥ 0, u(x, 0) = φ(x), u(0, t) = h(t) (0.2) for the Korteweg-de Vries-Burgers (KdV-B) equation. These… (More)

- M. D. Groves, S. M. Sun
- 2004

A model equation derived by B. B. Kadomtsev & V. I. Petviashvili (1970) suggests that the hydrodynamic problem for three-dimensional water waves with strong surface-tension effects admits a fully localised solitary wave which decays to the undisturbed state of the water in every horizontal spatial direction. This prediction is rigorously confirmed for the… (More)

The focus of the present study is the BBM equation which models unidirectional propagation of small amplitude long waves in shallow water and other dispersive media. Interest will be turned to the two-point boundary value problem wherein the wave motion is specified at both ends of a finite stretch of the medium of propagation. The principal new result is… (More)

- S. M. Sun
- SIAM J. Math. Analysis
- 2001

- M. D. Groves, M. Haragus, S. M. Sun
- 2001

The gravity-capillary water-wave problem concerns the irrotational flow of a perfect fluid in a domain bounded below by a rigid bottom and above by a free surface under the influence of gravity and surface tension. In the case of large surface tension the system has a travelling line solitary-wave solution for which the free surface has a localised profile… (More)

- M D Groves, M Haragus, S M Sun
- Philosophical transactions. Series A…
- 2002

The existence of a line solitary-wave solution to the water-wave problem with strong surface-tension effects was predicted on the basis of a model equation in the celebrated 1895 paper by D. J. Korteweg and G. de Vries and rigorously confirmed a century later by C. J. Amick and K. Kirchgässner in 1989. A model equation derived by B. B. Kadomtsev and V. I.… (More)

- S. M. Sun
- SIAM Journal of Applied Mathematics
- 1998

In this study, two Sxl gene homologs, designated as Mnsxl1 and Mnsxl2, were cloned and characterized from the freshwater prawn Macrobrachium nipponense by rapid amplification of cDNA ends. The deduced amino acid sequences of Mnsxl1 and Mnsxl2 showed high sequence homology to the insect Sxl and contained conserved domains in two RNA-binding motifs. Real-time… (More)

To assess the genetic status of this species, the genetic diversity of wild Macrobrachium nipponense from seven geographic locations in the Yellow River basin were investigated using 20 polymorphic microsatellite DNA loci. The genetic diversity between populations was indicated by the mean number of alleles per locus and mean observed heterozygosity (H) and… (More)