The travelling wave problem for a particular bidirectional Whitham system modelling surface water waves is under consideration. This firstly appeared in Dinvay et al. (2019), where it was numerically shown to be stable and good approximation the incompressible Euler equations. In subsequent papers (Dinvay, 2019; al., 2019) initial-value studied well-posedness classical Sobolev spaces proved. He...

We consider the ‘classical’ Boussinesq system of water wave theory, 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 horizontal channel. (We also consider its completely symmetric analog). We discretize the initial-boundary-value problem for these systems, corresponding to homogeneous Dirichlet boundary ...

In this Letter, we study Kaup-Boussinesq system by using the wellknown He’s variational approach. In fact, the He’s variational method is a promising method to various systems of linear and nonlinear equations.

We use the integrable Kaup-Boussinesq shallow water system, modified by a small viscous term, to model the formation of an undular bore with a steady profile. The description is made in terms of the corresponding integrable Whitham system, also appropriately modified by viscosity. This is derived in Riemann variables using a modified finite-gap integration technique for the Ablowitz-Kaup-Newell...

A model for intrinsic decoherence in quantum mechanics is proposed, based on a simple modification of unitary Schrodinger evolution. On sufticiently small time scales the system evolves by a random sequence of unitary phase changes generated by the Hamiltonian. The Schrodinger equation is obtained to zeroth order in the expansion parameter. Higher-order corrections lead to a loss of coherence i...

The improved Boussinesq equation is studied in this paper. Control properties for this equation posed on a bounded interval are first considered. When the control acts through the Dirichlet boundary condition the linearized system is proved to be approximately but not spectrally controllable. In a second part, the equation is posed on the one-dimensional torus and distributed moving controls ar...

Based on the homotopy perturbation method (HPM) and Padé approximants (PA), approximate and exact solutions are obtained for cubic Boussinesq and modified Boussinesq equations. The obtained solutions contain solitary waves, rational solutions. HPM is used for analytic treatment to those equations and PA for increasing the convergence region of the HPM analytical solution. The results reveal tha...

The incompressible Boussinesq equations not only have many applications in modeling fluids and geophysical fluids but also are mathematically important. The well-posedness and related problem on the Boussinesq equations have recently attracted considerable interest. This paper examines the global regularity issue on the 2D Boussinesq equations with fractional Laplacian dissipation and thermal d...