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 correspondent 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 ...

Riemann theta functions are used to construct one-periodic and two-periodic wave solutions to a class of (2 + 1)-dimensional Hirota bilinear equations. The basis for the involved solution analysis is the Hirota bilinear formulation, and the particular dependence of the equations on independent variables guarantees the existence of one-periodic and two-periodic wave solutions involving an arbitr...

The Hirota–Miwa equation (also known as the discrete KP equation, or the octahedron recurrence) is a bilinear partial difference equation in three independent variables. It is integrable in the sense that it arises as the compatibility condition of a linear system (Lax pair). The Hirota–Miwa equation has infinitely many reductions of plane wave type (including a quadratic exponential gauge tran...

The present paper is aimed to study an exact analysis of the free vibrations of a simply supported, homogeneous, transversely isotropic, cylindrical panel based on three-dimensional generalized theories of thermoelastic diffusion. After applying the displacement potential functions in the basic governing equations of generalized thermoelastic diffusion, it is noticed that a purely transverse mo...

We discuss the relation of a certain type of generalized Lyapunov equations to Gramians of stochastic and bilinear systems together with the corresponding energy functionals. While Gramians and energy functionals of stochastic linear systems show a strong correspondence to the analogous objects for deterministic linear systems, the relation of Gramians and energy functionals for bilinear system...

We consider a linear Schrödinger equation, on a bounded interval, with bilinear control, that represents a quantum particle in an electric eld (the control). We prove the exact controllability of this system, in any positive time, locally around the ground state. Similar results were proved for particular models [14, 15, 17], in non optimal spaces, in long time and the proof relied on the Nash-...

The analytical theory of one dimensional, dispersion free miscible displacement of oil by injection gas with nc component has shown that: the MMP is the lowest pressure at which any one of the initial oil, injection gas or crossover key tie lines becomes critical, which means that its length approaches to zero. In this paper, we propose a method for a solving multi component syst...

In previous work we introduced a construction to produce multiresolutions from given subdivisions. A portion of that construction required solving bilinear equations using a symbolic algebra system. Here we replace the bilinear equations with a pair of linear equation systems, resulting in a completely numerical construction. Diagrammatic tools provide assistance in carrying this out. The const...