This study investigates the numerical evolution of an initially internal random wave field characterized by a Gaussian spectrum shape using Benjamin–Ono (BO) equation. The research focuses on analyzing various properties associated with field, including transition to steady state spectra, statistical moments, and distribution functions amplitudes. Numerical simulations are conducted across diff...

Abstract We consider the third order Benjamin-Ono equation on torus ? t u = x ( ? 3 2 H ) + . prove that for any ? R , flow map continuously extends to r 0 s T if ? but does not admit a continuous extension 1 Moreover, we show is weakly sequentially in > L then classify traveling wave solutions and study their orbital stability.

Experimental results, such as NO2 hydrolysis and the hypergolicity of hydrazine/nitrogen tetroxide pair, have been interpreted in terms of NO2 dimers. Such interpretations are complicated by the possibility of several forms for the dimer: symmetric N2O4, cis-ONO-NO2, and trans-ONO-NO2. Quantum mechanical (QM) studies of these systems are complicated by the large resonance energy in NO2 which ch...

We propose a novel class of arbitrarily high-order mass or energy conservative numerical schemes for the generalized Benjamin–Ono equation on whole real line. The spatial discretization is achieved by pseudo-spectral method with rational basis functions. By reformulating discretized system into different equivalent forms, either semi-discretized can be preserved exactly under continuous time fl...

In this article, we establish new results about the ill-posedness of the Cauchy problem for the modified Korteweg-de Vries and the defocusing modified Korteweg-de Vries equations, in the periodic case. The lack of local well-posedness is in the sense that the dependence of solutions upon initial data fails to be continuous. We also develop a method for obtaining ill-posedness results in the per...

In this paper we propose a new approach to prove the local well-posedness of the Cauchy problem associated with strongly non resonant dispersive equations. As an example we obtain unconditional well-posedness of the Cauchy problem below H for a large class of one-dimensional dispersive equations with a dispersion that is greater or equal to the one of the Benjamin-Ono equation. Since this is do...

ONO-4007 is a synthetic analogue of the lipid A moiety of bacterial lipopolysaccharide, which exhibits antitumor activity by the induction of intratumoral tumor necrosis factor alpha, the potentiation of tumor-infiltrating macrophages, and the inhibition of angiogenesis. Interleukin (IL)-1 alpha, IL-6, and IL-12 induction by ONO-4007 activates cytotoxic natural killer cells to up-regulate IFN-g...