We consider the dynamics of even solutions one-dimensional nonlinear Klein-Gordon equation $\partial_t^2 \phi - \partial_x^2 + |\phi|^{2\alpha} =0$ for $\alpha>1$, in vicinity unstable soliton $Q$. Our main result is that stability energy space $H^1(\mathbb R)\times L^2(\mathbb R)$ implies asymptotic a local norm. In particular, there exists Lipschitz graph initial data leading to stable and as...

The Bethe-Salpeter amplitude $\mathrm{\ensuremath{\Phi}}(k,p)$ is expressed, by means of the Nakanishi integral representation, via a smooth function $g(\ensuremath{\gamma},z)$. This satisfies canonical equation $g=Ng$. However, calculations kernel $N$ in this equation, presented previously, were restricted to one-boson exchange and, depending on method, dealt with complex multivalued functions...

This note describes a numerically stable version of the improved Mellor–Yamada (M–Y) Level-3 model proposed by Nakanishi and Niino [Nakanishi, M. and Niino, H.: 2004, Boundary-Layer Meteorol. 112, 1–31] and demonstrates its application to a regional prediction of advection fog. In order to ensure the realizability for the improved M–Y Level-3 model and its numerical stability, restrictions are ...

Group signatures are generalized credential/member authentication schemes with wide applications, such as Trust Computing. Membership revocation problem is a major issue of group signatures. In some applications that group secret keys are stored in tamper resistant chips, a Verifier-Local Revocation resolution is more reasonable than other methods, such as witness based revocation. Boneh et al....

In this paper, we consider a 3d cubic focusing nonlinear Schrödinger equation (NLS) with slowly decaying potentials. Adopting the variational method of Ibrahim-Masmoudi-Nakanishi [12] , obtain condition for scattering. It is actually sharp in some sense since solution will blow up if it's false. The proof blow-up part relies on Du-Wu-Zhang [6] .

We consider the combined power-type nonlinear Schrödinger equations with energy-critical growth, and study solutions slightly above ground state threshold at low frequencies, so that we obtain a so-called nine-set theory developed by Nakanishi Schlag.