We have recently presented a method for solving the time-dependent Schrodinger equation by collocation on various members of a family of spatial grids and have shown that this method is interpretable in terms of the expansion of the wave function in a basis of discrete coordinate eigenfunctions. The method is applicable to molecular systems with one or multiple spatial dimensions, and also to b...

At the core of this article is an improved, sharp dispersive estimate for the anisotropic linear semigroup e1 arising in both the study of the dispersive SQG equation and the inviscid Boussinesq system. We combine the decay estimate with a blow-up criterion to show how dispersion leads to long-time existence of solutions to the dispersive SQG equation, improving the results obtained using hyper...

The nonlinear physical model such as the cubic nonlinear Schrodinger equation has been applied in many branches of physics. In this paper, the )) ( exp(    expansion method is applied to evaluate new exact travelling wave solutions of the complex Schrodinger equation with cubic nonlinearity. Various solutions of the cubic nonlinear Schrodinger equation using this method provide us the firm m...

In this paper we study the validity of the so-called Oberbeck-Boussinesq approximation for compressible viscous perfect gases in the whole three-dimensional space. Both the cases of fluids with positive heat conductivity and zero conductivity are considered. For small perturbations of a constant equilibrium, we establish the global existence of unique strong solutions in a critical regularity f...

We construct new integrable coupled systems of N = 1 supersymmetric equations and present integrable fermionic extensions of the Burgers and Boussinesq equations. Existence of infinitely many higher symmetries is demonstrated by the presence of recursion operators. Various algebraic methods are applied to the analysis of symmetries, conservation laws, recursion operators, and Hamiltonian struct...

In this paper we prove the global well-posedness of the two-dimensional Boussinesq system with zero viscosity for rough initial data.

This article concerns the existence of solutions to Schrodinger-Poisson system $$\displaylines{ -\Delta_p u+|u|^{p-2}u+\lambda\phi u=|u|^{q-2}u+h(x) \quad \hbox{in }\mathbb{R}^3,\\ -\Delta \phi=u^2 }\mathbb{R}^3, }$$ where \( 4/3 < p 12/5 \), q p^{*}=3p/(3-p) \(\Delta_p u =\hbox{div}(|\nabla u|^{p-2}\nabla u)\), \(\lambda >0\), and \(h \not= 0\). The multiplicity results are obtained by u...

In this paper we prove a global well-posedness result for tridimensional Navier-Stokes-Boussinesq system with axisymmetric initial data. This system couples Navier-Stokes equations with a transport equation governing the density.