In this paper we study the generalized BO-ZK equation in two space dimensionsWe review the existence theory for solitary waves and prove that they are nonlinearly unstable if p belongs to the range 4/3 < p < 4.We also establish Strichartz-type estimates.
This work studies the local well-posedness of the initial-value problem for the nonlinear sixthorder Boussinesq equation utt = uxx + βuxxxx + uxxxxxx + (u 2 )xx, where β = ±1. We prove local well-posedness with initial data in non-homogeneous Sobolev spaces H s (R) for negative indices of s ∈ R. Mathematical subject classification: 35B30, 35Q55, 35Q72. * Supported by FAPEMIG-Brazil and CNPq-Brazil.
This work studies the rotation-generalized Benjamin-Ono equation which is derived from the theory of weakly nonlinear long surface and internal waves in deep water under the presence of rotation. It is shown that the solitary-wave solutions are orbitally stable for certain wave speeds.Mathematical subject classification: 35Q35, 76B55, 76U05, 76B25, 35B35
We prove unique continuation results for the Kadomtsev–Petviashvili‐I and Benjamin–Ono–Zakharov–Kuznetsov equations. Our method of proof goes back to the complex variable techniques introduced by Bourgain. The approach is quite similar to that used by Panthee for the Kadomtsev–Petviashvili‐II and Zakharov–Kuznetsov equations.
Abstract. Here we consider results concerning ill-posedness for the Cauchy problem associated with the Benjamin-Ono-Zakharov-Kuznetsov equation, namely,
y).For k = 1, (IVP) is shown to be ill-posed in the class of anisotropic Sobolev spaces H s 1 ,s 2 (R 2 ), s 1 , s 2 ∈ R, while for k ≥ 2 ill-posedness is shown to hold in H s 1 ,s 2 (R 2 ), 2s 1 + s 2 < 3/2 − 2/k. Furthermore, for k = 2, 3, and some particular values of s 1 , s 2 , a stronger result is also established.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.