A bilinear Bäcklund transformation is presented for a (3 + 1)-dimensional generalized KP equation, which consists of six bilinear equations and involves nine arbitrary parameters. Two classes of exponential and rational traveling wave solutions with arbitrary wave numbers are computed, based on the proposed bilinear Bäcklund transformation. Published by Elsevier Ltd

In this paper, we first prove some local estimates for bilinear operators (closely related to the bilinear Hilbert transform and similar singular operators) with truncated symbol. Such estimates, in accordance with the Heisenberg uncertainty principle correspond to a description of " off-diagonal " decay. In addition they allow us to prove global continuities in Lebesgue spaces for bilinear ope...

In this work we prove Hardy space estimates for bilinear Littlewood-Paley-Stein square function and Calderón-Zygmund operators. Sufficient Carleson measure type conditions are given for square functions to be bounded from H p1 ×H p2 into Lp for indices smaller than 1, and sufficient BMO type conditions are given for a bilinear Calderón-Zygmund operator to be bounded from H p1 ×H p2 into H p for...

This paper considers the identi cation of time-invariant bilinear models using observed input{output data. Bilinear models represent a parsimonious class of nonlinear parameterisations and have been used in a variety of applications. However the performance of the bilinear model can be limited in practice when standard least-squares techniques are used, as this leads to biased parameter estimat...

In this paper, an efficient algorithm of logarithmic transformation to Hirota bilinear form of the KdV-type bilinear equation is established. In the algorithm, some properties of Hirota operator and logarithmic transformation are successfully applied, which helps to prove that the linear terms of the nonlinear partial differential equation play a crucial role in finding the Hirota bilinear form...

The study of bilinear operators associated to a class of non-smooth symbols can be reduced to the study of certain special bilinear cone operators to which a time frequency analysis using smooth wave-packets is performed. In this paper we prove that when smooth wave-packets are replaced by Walsh wave-packets the corresponding discrete Walsh model for the cone operators is not only Lp-bounded, a...

We consider model order reduction of bilinear descriptor systems using an interpolatory projection framework. Such nonlinear descriptor systems can be represented by a series of generalized linear descriptor systems (also called subsystems) by utilizing the Volterra-Wiener approach [22]. Standard projection techniques for bilinear systems utilize the generalized transfer function of these subsy...

In this paper, we first prove some local estimates for bilinear operators (closely related to the bilinear Hilbert transform and similar singular operators) with truncated symbol. Such estimates, in accordance with the Heisenberg uncertainty principle correspond to a description of “off-diagonal” decay. In addition they allow us to prove global continuities in Lebesgue spaces for bilinear opera...

The geometry of Rn is controlled algebraically by the dot product. We will abstract the dot product on Rn to a bilinear form on a vector space and study algebraic and geometric notions related to bilinear forms (especially the concept of orthogonality in all its manifestations: orthogonal vectors, orthogonal subspaces, and orthogonal bases). Section 1 defines a bilinear form on a vector space a...

This paper describes a technique for generating disjointly constrained bilinear programming test problems with known solutions and properties. The proposed construction technique applies a simple random tranformation of variables to a separable bilinear programming problem that is constructed by combining disjoint low-dimensional bilinear programs.