In the first part of this work we study local well-posedness dispersive equations in weighted spaces $$H^s({\mathbb {R}})\cap L^2(|x|^{2b}dx)$$ . We then apply our results for several models such as Hirota-Satsuma system, OST equation, Kawahara equation and a fifth-order model. Using these results, second is devoted to obtain related blow up system.

In this manuscript, we consider the internal control problem for fifth-order KdV type equation, commonly called Kawahara on unbounded domains. Precisely, under certain hypotheses over initial and boundary data, can prove that there exists an input such solutions of equation satisfy integral overdetermination condition. This condition is satisfied when domain posed in real line, left half-line, ...

We propose a novel algorithm, based on physics-informed neural networks (PINNs) to efficiently approximate solutions of nonlinear dispersive PDEs such as the KdV-Kawahara, Camassa-Holm andBenjamin-Ono equations. The stability these is leveraged prove rigorous bounds resulting error. present several numerical experiments demonstrate thatPINNs can very accurately

Department of Physics and Pre-Engineering Center for Research and Education in Optical Sciences and Applications Delaware State University, Dover, DE 19901-2277, USA Abstract The adiabatic parameter dynamics of solitons, due to the generalized Kawahara equation are obtained in this paper. The soliton perturbation theory is exploited to obtain the results. Also, the change in the velocity is obt...

Title The detection of carotid plaque rupture caused by intraplaque hemorrhage by serial high-resolution magnetic resonance imaging: a case report. Author(s) Kawahara, Ichiro; Nakamoto, Morito; Hayashi, Kentaro; Kitagawa, Naoki; Tsutsumi, Keisuke; Nagata, Izumi; Morikawa, Minoru; Hayashi, Tomayoshi Citation Surgical neurology, 70(6), pp.634-639; 2008 Issue Date 2008-12 URL http://hdl.handle.net...

Title The detection of carotid plaque rupture caused by intraplaque hemorrhage by serial high-resolution magnetic resonance imaging: a case report. Author(s) Kawahara, Ichiro; Nakamoto, Morito; Hayashi, Kentaro; Kitagawa, Naoki; Tsutsumi, Keisuke; Nagata, Izumi; Morikawa, Minoru; Hayashi, Tomayoshi Citation Surgical neurology, 70(6), pp.634-639; 2008 Issue Date 2008-12 URL http://hdl.handle.net...