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The noncommutative analogues of the nonisospectral Toda and Lotka-Volterra lattices are proposed and studied by performing nonisopectral deformations on the matrix orthogonal polynomials and matrix symmetric orthogonal polynomials without…

Exactly Solvable and Integrable Systems · Physics 2024-07-18 Anhui Yan , Chunxia Li

In this paper, we investigate the Noether symmetries of a generalized scalar-tensor, Brans-Dicke type cosmological model, in which we consider explicit scalar field dependent couplings to the Ricci scalar, and to the scalar field kinetic…

General Relativity and Quantum Cosmology · Physics 2016-02-03 J. A. Belinchón , T. Harko , M. K. Mak

Nonlinear dispersionless equations arise as the dispersionless limit of well know integrable hierarchies of equations or by construction, such as the system of hydrodynamic type. Some of these equations are integrable in the Hamiltonian…

Exactly Solvable and Integrable Systems · Physics 2015-06-26 J. C. Brunelli

We propose the Hirota bilinearization of the Fokas-Lenells derivative nonlinear Schrodinger equation with a non-vanishing background. The bilinear method is applied using an auxilary function to obtain the dark one soliton solution, dark…

Exactly Solvable and Integrable Systems · Physics 2024-02-13 Riki Dutta , Sagardeep Talukdar , Gautam Kumar Saharia , Sudipta Nandy

In the paper we continue to consider symmetries related to the Ablowitz-Ladik hierarchy. We derive symmetries for the integrable discrete nonlinear Schr\"odinger hierarchy and discrete AKNS hierarchy. The integrable discrete nonlinear…

Exactly Solvable and Integrable Systems · Physics 2010-04-08 Da-jun Zhang , Shou-ting Chen

The Arecchi-Bonifacio (or Maxwell-Bloch) model is the benchmark for the description of active optical media. However, in the presence of a fast relaxation of the atomic polarization, its implementation is a challenging task even in the…

Optics · Physics 2023-03-03 Antonio Politi , Serhiy Yanchuk , Giovanni Giacomelli

We consider a class of $N=2$ supersymmetric non--unitary theories in two--dimensional Minkowski spacetime which admit classical solitonic solutions. We show how these models can be twisted into a topological sector whose energy--momentum…

High Energy Physics - Theory · Physics 2009-10-22 S. Penati , M. Pernici , D. Zanon

A short overview of the billiard approach for cosmological-type models with n Einstein factor-spaces is presented. We start with the billiard representation for pseudo-Euclidean Toda-like systems of cosmological origin. Then we consider…

High Energy Physics - Theory · Physics 2009-03-19 V. D. Ivashchuk , V. N. Melnikov

In this letter we examine the two-component Hirota (TH) equations which describes the pulse propagation in a coupled fiber with higher-order dispersion and self-steepening. As the TH equations is a complete integrable system, which admits a…

Analysis of PDEs · Mathematics 2018-09-20 Fang Fang , Beibei Hu , Ling Zhang , Ning Zhang

A method is proposed to systematically generate solutions of the two-dimensional Toda lattice equation in terms of previously known solutions $\phi\left(x,y\right)$ of the two-dimensional Laplace's equation. The two-dimensional solution of…

Exactly Solvable and Integrable Systems · Physics 2020-12-02 Vinicius Duarte

In this paper, we firstly construct a weakly coupled Toda lattices with indefinite metrics which consist of $2N$ different coupled Hamiltonian systems. Afterwards, we consider the iso-spectral manifolds of extended tridiagonal Hessenberg…

Exactly Solvable and Integrable Systems · Physics 2020-05-07 Jian Li , Chuanzhong Li

We consider a generalization of the full symmetric Toda hierarchy where the matrix $\tilde {L}$ of the Lax pair is given by $\tilde {L}=LS$, with a full symmetric matrix $L$ and a nondegenerate diagonal matrix $S$. The key feature of the…

solv-int · Physics 2015-06-26 Yuji Kodama , Jian Ye

In this paper, we consider the following elliptic Toda system associated to a general simple Lie algebra with multiple singular sources \begin{equation*} \begin{cases} -\Delta…

Analysis of PDEs · Mathematics 2019-04-12 Ali Hyder , Juncheng Wei , Wen Yang

We consider a class of fully nonlinear second order elliptic equations on Hermitian manifolds closely related to the general notion of $\bfG$-plurisubharmonicity of Harvey-Lawson and an equation treated by Sz\'ekelyhidi-Tosatti-Weinkove in…

Analysis of PDEs · Mathematics 2021-10-04 Mathew George , Bo Guan , Chunhui Qiu

Bilinearization of a given nonlinear partial differential equation is very important not only to find soliton solutions but also to obtain other solutions such as the complexitons, positons, negatons, and lump solutions. In this work we…

Exactly Solvable and Integrable Systems · Physics 2023-04-14 Metin Gürses , Aslı Pekcan

A multidimensional field model describing the behaviour of (at most) one Einstein space of non-zero curvature and n Ricci-flat internal spaces is considered. The action contains several dilatonic scalar fields and antisymmetric forms. The…

General Relativity and Quantum Cosmology · Physics 2007-05-23 K. A. Bronnikov , M. A. Grebeniuk , V. D. Ivashchuk , V. N. Melnikov

A generalized inhomogeneous higher-order nonlinear Schrodinger (GIHNLS) equation for the Heisenberg ferromagnetic spin chain system in (1+1)-dimensions under zero boundary condition at infinity is taken into account. The spectral analysis…

Exactly Solvable and Integrable Systems · Physics 2022-08-26 Zhou-Zheng Kang , Rong-Cao Yang

A new class of integrable two-dimensional dilaton gravity theories, in which scalar matter fields satisfy the Toda equations, is proposed. The simplest case of the Toda system is considered in some detail, and on this example we outline how…

High Energy Physics - Theory · Physics 2008-03-31 A. T. Filippov

Various solutions to the discrete Schwarzian KdV equation are discussed. We first derive the bilinear difference equations of Hirota type of the discrete Schwarzian KP equation, which is decomposed into three discrete two-dimensional Toda…

Exactly Solvable and Integrable Systems · Physics 2015-03-18 Mike Hay , Kenji Kajiwara , Tetsu Masuda

In this paper, we use Hirota's bilinear method to directly construct periodic wave solutions of nonlinear equations. The asymptotic property of periodic wave solutions are analyzed. It is shown that well-known soliton solutions can be…

Exactly Solvable and Integrable Systems · Physics 2016-09-08 H. H. Dai , E. G. Fan X. G. Geng