The Boussinesq system arises in Fluid Mechanics when motion is governed by density gradients caused by temperature or concentration di erences. In the former case, and when thermodynamical coe cients are regarded as temperature dependent, the system consists of the Navier-Stokes equations and the non linear heat equation coupled through the viscosity, bouyancy and convective terms. In this pape...

Mark Kac [“Can one hear the shape of drums?” Am. Math. Monthly 73, l-23 (1966)] asked if the shape of a region fiCR” could be determined from its sound (spectrum of the Laplacian A,). He proved the conjecture for special classes of domains, including polygons and balls in W”. Similar problems could be raised in other geometric contexts, including “shape of metric” for Laplacians on manifolds or...

We prove the existence and uniqueness of smooth solutions with large initial data for a system equations modeling interaction short waves, governed by nonlinear Schrodinger equation, an...

Depth-integrated long-wave models, such as the shallow-water and Boussinesq equations, are standard fare in the study of small amplitude surface waves in shallow water. While the shallow-water theory features conservation of mass, momentum and energy for smooth solutions, mechanical balance equations are not widely used in Boussinesq scaling, and it appears that the expressions for many of thes...

Standard perturbation methods are applied to Euler’s equations of motion governing the capillary-gravity shallow water waves to derive a general higher-order Boussinesq equation involving the small-amplitude parameter, α = a/h0, and long-wavelength parameter, β = (h0/l), where a and l are the actual amplitude and wavelength of the surface wave, and h0 is the height of the undisturbed water surf...

A new computational method for determining the eigenvalues and eigenfunctions of the Schrodinger equation is described. Conventional methods for solving this problem rely on diagonalization of a Hamiltonian matrix or iterative numerical solutions of a time independent wave equation. The new method, in contrast, is based on the spectral properties of solutions to the time-dependent Schrodinger e...

Considered herein are a number of variants of the classical Boussinesq system and their higher-order generalizations. Such equations were first derived by Boussinesq to describe the two-way propagation of small-amplitude, long wavelength, gravity waves on the surface of water in a canal. These systems arise also when modeling the propagation of long-crested waves on large lakes or the ocean and...

This paper is concerned with the local well-posedness of Oberbeck Boussinesq approximation for unsteady motion a drop in another fluid separated by closed interface surface tension. We are devoted to obtaining linearized Oberbeck-Boussinesq fixed domain using Hanzawa transformation, and maximal $ L^{p} $-$ L^{q} regularities two-phase system obtained authors [10] establish existence uniqueness ...

This paper considers the existence and stability of traveling wave solutions Boussinesq–Burgers system describing propagation bores. Assuming fluid is weakly dispersive, we establish three different profiles by geometric singular perturbation theory alongside phase plane analysis. We further employ method weighted energy estimates to prove nonlinear asymptotic against small perturbations. The t...