By using the first and second flows of Kowalevski top, we can make top into two which has time variales. Then show that equations become those full genus Jacobi inversion problem. In addition to Lax pair for flow, costruct flow. Using flows, Lie group structure these pairs is Sp(4,$\mathbb{R}$) $\cong$ SO(3,2). Through conclude hyperelliptic function

Properties of dust-ion acoustic waves (DIAWs) in an unmagnetized dusty plasma consisting mobile ions, superthermal electrons, and negatively charged dust clouds with charge fluctuation are investigated. Burgers’ equation is derived from the fluid plasmas by considering reductive perturbation technique. The Lax pair evolution obtained, characteristics DIAWs investigated employing Darboux transfo...

We present a generalized study and characterization of the integrability properties derivative non-linear Schrödinger equation in 1+1 dimensions. A Lax pair is derived for this by means Miura transformation singular manifold method. This procedure, together with Darboux transformations, allow us to construct wide class rational soliton-like solutions. Clasical Lie symmetries have also been comp...

Abstract We study integrability properties of the non-chiral intermediate long wave (ncILW) equation with periodic boundary conditions. The ncILW was recently introduced by authors as a parity-invariant relative equation. For this new we: (a) derive Lax pair, (b) Hirota bilinear form, (c) use method to construct family exact solutions, (d) Bäcklund transformation, (e) transformation obtain an i...

In this paper, we obtain the long-time asymptotics of complex mKdV equation via Defit-Zhou method (Non-linear steepest descent method). The Cauchy problem is transformed into corresponding Riemann-Hilbert on basis Lax pair and scattering matrix. After that problems are converted through a decomposition matrix-valued spectral function factorizations jump matrix for problem. Finally, by solving l...

We give a new derivation and characterisation of the generalised elliptic genus of Krichever-Höhn by means of a functional equation. Introduction Functional equations provide a common thread to several investigations in mathematics and physics: our focus in this article will particularly be on the areas of topology and integrable systems where it is still unclear whether the threads before us f...

Liftings of endofunctors on sets to relations are commonly used capture bisimulation coalgebras. Lax versions have been in those cases where strict lifting fails bisimilarity, as well modeling other notions simulation. This paper provides tools for defining and manipulating lax liftings. As a central result, we define notion distributive law functor over the powerset monad, show that there is a...

It is shown that the problem of reduction can be formulated in a uniform way using the theory of invariants. This provides a powerful tool of analysis and it opens the road to new applications of these algebras, beyond the context of integrable systems. Moreover, it is proven that sl2(C)–Automorphic Lie Algebras associated to the icosahedral group I, the octahedral group O, the tetrahedral grou...

The Q1 lattice equation, a member in the Adler-Bobenko-Suris list of 3D consistent lattices, is investigated. By using multidimensional consistency, novel Lax pair for equation given, which can be nonlinearised to produce integrable symplectic maps. Consequently, Riemann theta function expression discrete potential derived with help Baker-Akhiezer functions. This leads algebro-geometric integra...