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In this paper, we derive n-fold Darboux transformation of the two-component Hirota and the Maxwell-Bloch(TH-MB) equations and its determinant representation. Using Darboux determinant representation, we provide soliton solutions, positon…

Exactly Solvable and Integrable Systems · Physics 2013-10-03 Jieming Yang , Chuanzhong Li , Tiantian Li , Zhaoneng Cheng

Liouville field theory on an unoriented surface is investigated, in particular, the one point function on a RP^2 is calculated. The constraint of the one point function is obtained by using the crossing symmetry of the two point function.…

High Energy Physics - Theory · Physics 2009-11-07 Yasuaki Hikida

The twice-dimensionally reduced Seiberg-Witten monopole equations admit solutions depending on two real parameters (b,c) and an arbitrary analytic function f(z) determining a solution of Liouville's equation. The U(1) and manifold curvature…

High Energy Physics - Theory · Physics 2009-10-30 C. Saclioglu , S. Nergiz

We establish Liouville type theorems for degenerate conformally invariant equations.

Analysis of PDEs · Mathematics 2007-05-23 YanYan Li

Isothermic surfaces are surfaces which allow a conformal curvature line parametrisation. They form an integrable system, and Darboux transforms of isothermic surfaces obey Bianchi permutability: for two distinct spectral parameters the…

Differential Geometry · Mathematics 2022-05-31 Joseph Cho , Katrin Leschke , Yuta Ogata

We study the Liouville type theorems for transversally harmonic and biharmonic maps on foliated Riemannian manifolds

Differential Geometry · Mathematics 2016-06-30 Min Joo Jung , Seoung Dal Jung

Suggestions concerning the generalization of the geometric quantization to the case of nonlinear field theories are given. Results for the Liouville field theory are presented.

dg-ga · Mathematics 2007-05-23 Wlodzimierz Piechocki

In this article, we investigate the incompressible 2D Euler equations on a rotating biaxial ellipsoid, which model the dynamics of the atmosphere of a Jovian planet. We study the non-zonal Rossby-Haurwitz solutions of the Euler equations on…

Analysis of PDEs · Mathematics 2023-10-30 Chenghao Xu

Two types of soliton solutions are analytically considered in a rhombic onedimensional lattice: transverse (discrete) solitons and longitudinal solitons. Based on the multi-scale method, longitudinal solitons are obtained as envelopes of…

Pattern Formation and Solitons · Physics 2025-06-10 Shaykin Dmitriy

The paper describes relations between Liouville type theorems for solutions of a periodic elliptic equation (or a system) on an abelian cover of a compact Riemannian manifold and the structure of the dispersion relation for this equation at…

Mathematical Physics · Physics 2007-09-03 Peter Kuchment , Yehuda Pinchover

All Darboux integrable difference equations on the quad-graph are described in the case of the equations that possess autonomous first-order integrals in one of the characteristics. A generalization of the discrete Liouville equation is…

Exactly Solvable and Integrable Systems · Physics 2017-12-04 S. Ya. Startsev

We use the variational method to obtain approximate analytical expressions for the stationary pulselike solutions in birefringent fibers when differences in both phase velocities and group velocities between the two components and rapidly…

Optics · Physics 2016-06-29 N. J. Rodriguez-Fernandez , J. M. Soto-Crespo

Using bidifferential calculus, we derive a vectorial binary Darboux transformation for an integrable matrix version of the first negative flow of the Kaup-Newell hierarchy. A reduction from the latter system to an integrable matrix version…

Exactly Solvable and Integrable Systems · Physics 2026-02-12 Folkert Müller-Hoissen , Rusuo Ye

In this letter, for the discrete parity-time-symmetric nonlocal nonlinear Schr\"{o}dinger equation, we construct the Darboux transformation, which provides an algebraic iterative algorithm to obtain a series of analytic solutions from a…

Exactly Solvable and Integrable Systems · Physics 2016-11-02 Tao Xu , Hengji Li , Hongjun Zhang , Min Li , Sha Lan

The paper contains integral representations for certain classes of exponentially growing solutions of second order periodic elliptic equations. These representations are the analogs of those previously obtained by S. Agmon, S. Helgason, and…

Analysis of PDEs · Mathematics 2007-05-23 Peter Kuchment , Yehuda Pinchover

In this paper, we construct a generalized Darboux transformation to the coupled Hirota equations with high-order nonlinear effects like the third dispersion, self-steepening and inelastic Raman scattering terms. As application, an Nth-order…

Mathematical Physics · Physics 2014-04-29 Xin Wang , Yuqi Li , Yong Chen

We derive a permutability theorem for the Christoffel, Goursat and Darboux transformations of isothermic surfaces. As a consequence we obtain a simple proof of a relation between Darboux pairs of minimal surfaces in Euclidean space, curved…

Differential Geometry · Mathematics 2016-02-23 U. Hertrich-Jeromin , A. Honda

In this study we work on a novel Hamiltonian system which is Liouville integrable. In the integrable Hamiltonian model, conserved currents can be represented as Binomial polynomials in which each order corresponds to the integral of motion…

Exactly Solvable and Integrable Systems · Physics 2023-04-11 Mustafa Mullahasanoglu

We construct one soliton solutions for the nonlinear Schroedinger equation with variable quadratic Hamiltonians in a unified form by taking advantage of a complete (super) integrability of generalized harmonic oscillators. The soliton wave…

Mathematical Physics · Physics 2010-11-25 Erwin Suazo , Sergei K. Suslov

We study traveling wave solutions of an equation for surface waves of moderate amplitude arising as a shallow water approximation of the Euler equations for inviscid, incompressible and homogenous fluids. We obtain solitary waves of…

Classical Analysis and ODEs · Mathematics 2013-12-06 Armengol Gasull , Anna Geyer