Related papers: Lagrangian multiform structure for the lattice KP …
A pluri-Lagrangian (or Lagrangian multiform) structure is an attribute of integrability that has mainly been studied in the context of multidimensionally consistent lattice equations. It unifies multidimensional consistency with the…
A Lagrangian multiform structure is established for a generalisation of the Darboux system describing orthogonal curvilinear coordinate systems. It has been shown in the past that this system of coupled PDEs is in fact an encoding of the…
A variational structure for the potential AKP system is established using the novel formalism of a Lagrangian multiforms. The structure comprises not only the fully discrete equation on the 3D lattice, but also its semi-discrete variants…
We show that well-chosen Lagrangians for a class of two-dimensional integrable lattice equations obey a closure relation when embedded in a higher dimensional lattice. On the basis of this property we formulate a Lagrangian description for…
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…
We develop the concept of pluri-Lagrangian structures for integrable hierarchies. This is a continuous counterpart of the pluri-Lagrangian (or Lagrangian multiform) theory of integrable lattice systems. We derive the multi-time Euler…
Lagrangian multiforms provide a variational framework for describing integrable hierarchies. This thesis presents two approaches for systematically constructing Lagrangian one-forms, which cover the case of finite-dimensional integrable…
We present recent developments on geometric theory of the Hirota system and of the non-commutative discrete Kadomtsev-Petviashvili (KP) hierarchy adding also some new results which make the picture more complete. We pay special attention to…
Many integrable hierarchies of differential equations allow a variational description, called a Lagrangian multiform or a pluri-Lagrangian structure. The fundamental object in this theory is not a Lagrange function but a differential…
A pluri-Lagrangian structure is an attribute of integrability for lattice equations and for hierarchies of differential equations. It combines the notion of multi-dimensional consistency (in the discrete case) or commutativity of the flows…
We present a new form of the multi-boson reduction of KP hierarchy with Lax operator written in terms of boson fields abelianizing the second Hamiltonian structure. This extends the classical Miura transformation and the Kupershmidt-Wilson…
Inspired by the forms of delay-Painleve equations, we consider some new differential-discrete systems of KdV, mKdV and Sine-Gordon - type related by simple one way Miura transformations to classical ones. Using Hirota bilinear formalism we…
The lattice Gel'fand-Dikii hierarchy was introduced by Nijhoff, Papageorgiou, Capel and Quispel in 1992 as the family of partial difference equations generalizing to higher rank the lattice Korteweg-de Vries systems, and includes in…
We introduce a class of reductions of the two-component KP hierarchy, which includes the Hirota-Ohta system hierarchy. The description of the reduced hierarchies is based on the Hirota bilinear identity and an extra bilinear relation…
We establish connections between two cascades of integrable systems generated from the continuum limits of the Hirota-Miwa equation and its remarkable nonlinear counterpart under the Miwa transformation respectively. Among these equations,…
We present a hierarchy of discrete systems whose first members are the lattice modified Korteweg-de Vries equation, and the lattice modified Boussinesq equation. The N-th member in the hierarchy is an N-component system defined on an…
It is quite basic in integrable systems to deriving Lax equations from bilinear equations. For multi--component KP theory, corresponding Lax structures are mainly constructed by matrix pseudo-differential operators for fixed discrete…
In a previous paper by one of the authors, a Lagrangian 3-form structure was established for a generalised Darboux system, originally describing orthogonal curvilinear coordinate systems, which encodes the Kadomtsev-Petviashvili (KP)…
We consider (3+1)-dimensional second-order evolutionary PDEs where the unknown $u$ enters only in the form of the 2nd-order partial derivatives. For such equations which possess a Lagrangian, we show that all of them have a symplectic…
A space discretization of an integrable long wave-short wave interaction model, called the Yajima-Oikawa system, was proposed in the recent paper arXiv:1509.06996 using the Hirota bilinear method (see also…