It is shown that, by letting wavenumbers and frequencies complex in Hirota’s bilinear method, new classes of exact solutions of soliton equations can be obtained systematically. They include not only singular or N -homoclinic solutions but also N -wavepacket solutions. PACS: 03.40.Kf, 47.35.+i

this paper has been devoted to apply the reconstruction of variational iteration method (rvim) to handle the systems of integro-differential equations. rvim has been induced with laplace transform from the variational iteration method (vim) which was developed from the inokuti method. actually, rvim overcome to shortcoming of vim method to determine the lagrange multiplier. so that, rvim method...

In a companion paper ( arXiv:1910.03150 ) to this one, we proved that the Gromov–Witten theory of Fano orbifold line type D is governed by system Hirota Bilinear Equations. The goal prove every solution Equations determines new integrable hierarchy Lax equations. We suggest name extended D-Toda for equations, because it should be viewed as analogue Carlet’s bi-graded Toda hierarchy, which known...

The Ablowitz-Ladik hierarchy (ALH) is considered in the framework of the inverse scattering approach. After establishing the structure of solutions of the auxiliary linear problems , the ALH, which has been originally introduced as an infinite system of difference-differential equations is presented as a finite system of difference-functional equations. The representation obtained, when rewritt...

Abstract: This paper presents the development of a new model reduction method for discrete-time bilinear systems based on the balanced truncation framework. In many model reduction applications, it is advantageous to analyze the characteristics of the system with emphasis on particular frequency intervals of interest. In order to analyze the degree of controllability and observability of discre...

We develop a Hamiltonian discontinuous finite element discretization of a generalized Hamiltonian system for linear hyperbolic systems, which include the rotating shallow water equations, the acoustic and Maxwell equations. These equations have a Hamiltonian structure with a bilinear Poisson bracket, and as a consequence the phase-space structure, “mass” and energy are preserved. We discretize ...