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

A bilinear selection scheme for ranked populations is presented. The deVelopment of the selection scheme is motivated by the desire for a generationally dependant selection mechanism that can be adjusted in an intuitive manner. The selection mechanism is dehned by a four parameter (p, l, c, B) bilinear cumulative probabiliry distribution. Expressions for the mean and variance of the proposed bi...

This paper presents an overview of several gradienttype recursive algorithms for adaptive nonlinear filters equipped with bilinear system models. Bilinear models are attractive because they can approximate a large class of nonlinear systems with great parsimony in the use of coefficients. Two algorithms of complexity O(N3) (N is the memory span of the bilinear system model used in the adaptive ...

We present a computational framework for recovering both 1 st-order motion parameters (observer direction of translation and observer rotation), 2 nd-order motion parameters (observer rotational acceleration) and relative depth maps from time-varying optical ow. We recover translation speed and acceleration in units which are scaled relative to the distance to the object. Our assumption is that...

and Applied Analysis 3 From the corresponding facts in the Aronszajn-Kolmogorov theorem of 17 , we have the following result. Lemma 2.3 see 17 . Let A be a σ-C∗-algebra,H a Hilbert space, and a map T : A ×A → B H be given such that, for all a1, a2, . . . , an ∈ A, [ T ( ai , aj )]n i,j 1 ∈ M n B H . 2.3 Then there exists a Hilbert space K and a map V : A → B H,K such that T a, b V a∗ ∗V b , ∀a,...

For the Kac-Wakimoto hierarchy constructed from the principal vertex operator realization of the basic representation of the affine Lie algebra D (1) n , we compute the coefficients of the corresponding Hirota bilinear equations, and verify the coincidence of these bilinear equations with the ones that are satisfied by Givental’s total descendant potential of the Dn singularity, as conjectured ...

A meshless numerical technique is proposed for solving the generalized variable coefficient Schrodinger equation and Schrodinger-Boussinesq system with electromagnetic fields. The employed meshless technique is based on a generalized smoothed particle hydrodynamics (SPH) approach. The spatial direction has been discretized with the generalized SPH technique. Thus, we obtain a system of ordinary...