We extend the well-known trace formula for Hill's equation to general one-dimensional Schrodinger operators. The new function <J , which we introduce, is used to study absolutely continuous spectrum and inverse problems. In this note we will consider one-dimensional Schrodinger operators d2 (IS) H = -j-1 + V(x) onL2(R;dx)

We establish the existence and uniqueness for Boussinesq system in ℝ 3 critical space

We consider the Oberbeck–Boussinesq system with non-local boundary conditions arising as a singular limit of full Navier–Stokes–Fourier in regime low Mach and Froude numbers. The existence strong solutions is shown on maximal time interval <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="left-bracket 0 comma upper T Subscript normal m...

In this paper, we are concerned with the generalized Boussinesq equation including the singularly sixth-order Boussinesq equation, which describes the bi-directional propagation of small amplitude and long capillary-gravity waves on the surface of shallow water for bond number less than but very close to 1/3. By the means of two proper ansatzs, we obtain explicit traveling solitary wave solutio...