In this paper we consider the one-parameter family of Bona-Smith systems, which belongs to the class of Boussinesq systems modelling two-way propagation of long waves of small amplitude on the surface of water in a channel. We study three initial-boundary-value problems for these systems, corresponding, respectively, to nonhomogeneous Dirichlet, reflection, and periodic boundary conditions pose...

Diophantine criteria occur naturally in the theory of partial differential equations through the notorious problem of small denominators. An extensive treatment of such problems in the theory of PDEs can be found, e.g., in [6]. In this paper, we are interested in a Diophantine problem related to an inhomogeneous wave equation in n spatial and one temporal dimension with periodic boundary condit...

The Korteweg-de Vries (KdV) equation with periodic boundary conditions is considered. The interaction of a periodic solitary wave (cnoidal wave) with high frequency radiation of finite energy (L-norm) is studied. It is proved that the interaction of low frequency component (cnoidal wave) and high frequency radiation is weak for finite time in the following sense: the radiation approximately sat...

Let f be an integrable function on an infinite measure space (S,S , π). We show that if a regenerative sequence {Xn}n≥0 with canonical measure π could be generated then a consistent estimator of λ ≡ ∫ S fdπ can be produced. We further show that under appropriate second moment conditions, a confidence interval for λ can also be derived. This is illustrated with estimating countable sums and inte...

In [2], two of the authors and W. Meeks found examples of translation-invariant, embedded minimal surfaces with an infinite number of topological ends. For each k > 0, a surfaceMk was constructed, which was invariant with respect to a translation parallel to the x3-axis, and under a rotation group of order k+ 1 around the x3-axis. The method of construction was generalized in [3] to obtain the ...

Huang and Zhang cite{Huang} have introduced the concept of cone metric space where the set of real numbers is replaced by an ordered Banach space. Shojaei cite{shojaei} has obtained points of coincidence and common fixed points for s-Contraction mappings which satisfy generalized contractive type conditions in a complete cone metric space.In this paper, the notion of complete cone metric ...