Keywords: (3 + 1)-dimensional Jimbo–Miwa equation Hirota bilinear form Wronskian determinant solution a b s t r a c t In this paper, we obtain two kinds of sufficient conditions consisting of systems of linear partial differential equations, which guarantee that the corresponding Wroskian determinant solves the (3 + 1)-dimensional Jimbo–Miwa equation in the Hirota bilinear form. Our results sug...

the role in clinical anesthesia. Anesthesiology 1991; 74: 581±605 16 Angel A, Majeed AB. Alterations of `sleeping time' in the rat induced by drugs which modulate central monoaminergic systems. Br J Anaesth 1990; 64: 594±600 17 Mason ST, Angel A. Brain noradrenaline and anaesthesia: further characterization of the beta-receptor. Neuropharmacology 1983; 22: 1065±9 18 Smart D. Orexins: a new fami...

Extending the gauge-invariance principle for τ functions of the standard bilinear formalism to the supersymmetric case, we define N = 1 supersymmetric Hirota operators. Using them, we bilinearize SUSY nonlinear evolution equations. The super-soliton solutions and extension to SUSY sine-Gordon are also discussed. As a quite strange paradox it is shown that the Lax integrable SUSY KdV of Manin-Ra...

The paper is a review of recent works devoted to analysis of classical integrable structures in quantum integrable models solved by one or another version of the Bethe ansatz. Similarities between elements of the quantum and classical theories of integrable systems are discussed. Some key notions of the quantum theory, now standard in the quantum inverse scattering method, are identiied with ty...

The Hirota equation is an integrable higher order nonlinear Schr\"{o}dinger type which describes the propagation of ultrashort light pulses in optical fibers. We present a standard Darboux transformation for and then construct its quasideterminant solutions. multisoliton breather solutions are given explicitly.

The Hirota variety parameterizes solutions to the KP equation arising from a degenerate Riemann theta function. In this work, we study in detail rational nodal curve. Of particular interest is irreducible subvariety defined as image of parameterization map, call main component. Proving that an component corresponds solving weak Schottky problem for curves. We solve up genus nine using computati...

The coupled KP hierarchy, introduced by Hirota and Ohta, are investigated by using the dressing method. It is shown that the coupled KP hierarchy can be reformulated as a reduced case of the 2-component KP hierarchy.

In the frame of the exactly integrable model of the 1D crystal — Hirota lattice model — the dynamics and interaction of the discrete breathers has been considered. These high-frequency localized nonlinear excitations elastically interact with each other and with such excitations as shock and linear waves. Using the nonlinear superposition formula the pair collision processes of the excitations ...