In this paper, the generalized (2+1)-dimensional Calogero-Bogoyavlenskii-Schiff (shortly CBS) equations are investigated. We employ the Hirota’s bilinear method to obtain the bilinear form of CBS equations. Then by the idea of extended homoclinic test approach (shortly EHTA), some exact soliton solutions including breather type solutions are presented. Keywords—EHTA, (2+1)-dimensional CBS equat...

This paper shows that several integrable lattices can be transformed into coupled bilinear differential-difference equations by introducing auxiliary variables. By testing the Bäcklund transformations for this type of coupled bilinear equations, a new integrable lattice is found. By using the Bäcklund transformation, soliton solutions are obtained. By the dependent variable transformation, this...

Recent studyoncertificateless authenticated key agreement focuses on bilinear pairing-freecertificateless authenticated key agreement protocol. Yet it has got limitations in the aspect of computational amount.So it is important to reduce the number of the scalar multiplication over elliptic curve group in bilinear pairing-free protocols. This paper proposed a new bilinear pairing-freecertificat...

Optimal conditions are used in nondynamical formalism to diagonalize the pionproton reaction matrix as much as possible. Invariance laws are imposed to simplify the relationship between observables and bilinear combination of amplitudes. Transverse amplitudes are determined by using measured polarization parameter in xfp elastic scattering at 6.0 GeVIC

We consider an economical bilinear rectangular mixed finite element scheme on regular mesh for generalized Newtonian flows, where the viscosity obeys a Carreau type law for a pseudo-plastic. The key issue in the scheme is that the two components of the velocity and the pressure are defined on different meshes. Optimal error bounds for both the velocity and pressure are obtained by proving a dis...

In this paper, we construct the bilinear identities for wave functions of an extended Kadomtsev-Petviashvili (KP) hierarchy, which is KP hierarchy with particular flows (2008, Phys. Lett. A, 372: 3819). By introducing auxiliary parameter (denoted by $z$), whose flow corresponds to so-called squared eigenfunction symmetry find tau-function hierarchy. It shown that will generate all Hirota's equa...

In this paper, we are interested in the construction of a bilinear pseudodifferential calculus. We define some symbolic classes which contains those of Coifman-Meyer. These new classes allow us to consider operators closely related to the bilinear Hilbert transform. We give a description of the action of our bilinear operators on Sobolev spaces. These classes also have a “nice” behavior through...

This article is concerned with the question of whether Marcinkiewicz multipliers on R2n give rise to bilinear multipliers on R×R. We show that this is not always the case. Moreover, we find necessary and sufficient conditions for such bilinear multipliers to be bounded. These conditions in particular imply that a slight logarithmic modification of the Marcinkiewicz condition gives multipliers f...