# Finite Genus Solutions To The Ablowitz‐Ladik Equations

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### Soliton fay identities: II. Bright soliton case

Sep 25, 2019 approach to the integrable equations. The classical Fay identities [8, 9] have been derived for the theta-functions associated with compact Riemann surfaces of the ﬁnite genus. It is a known fact that the so-called ﬁnite-gap solutions for integrable equations (which are built of these theta-functions) can be

### Doctoral Degrees Conferred - AMS

ferential equations with applications to mathematical neurosciences. University of Arizona (11) Mathematics Lozano, Guadalupe, Poisson geometry of the Ablowitz-Ladik equations. Perlis, Alexander, The projective geom-etry of curves of genus one, and an algorithm for the jacobian of such a curve. Shipmar, Patrick, Plant patterns. Program in

### Doctoral Degrees Conferred

ferential equations with applications to mathematical neurosciences. University of Arizona (11) Mathematics Lozano, Guadalupe, Poisson geometry of the Ablowitz-Ladik equations. Perlis, Alexander, The projective geom-etry of curves of genus one, and an algorithm for the jacobian of such a curve. Shipmar, Patrick, Plant patterns. Program in

### µ v o } ( E } v o ] v D Z u ] o W Z Ç ]

Finite genus solutions to the lattice Schwarzian Korteweg-de Vries equation Xiaoxue Xu School of Mathematics and Statistics, Zhengzhou University, Zhengzhou, 450001, People s Republic of China [email protected] Cewen Cao School of Mathematics and Statistics, Zhengzhou University, Zhengzhou, 450001, People s Republic of China [email protected]

### PHYSICA - Mathematics U-M LSA

2. Antiperiod 2 solutions of the Ablowitz-Ladik equations The system of ordinary differential equations ( 1 ) has a class of exact solutions satisfying spatially antiperiod 2 boundary conditions, Qn+2(t)=-Qn(t), Rn+2(t)=-Rn(t). (4) These exact solutions are very simple by virtue of the structure of the nonlinear terms.

### MACROSCOPIC BEHAVIOR IN THE ABLOWITZ-LADIK EQUATIONS

Preprint of an article appearing in Nonlinear Evolution Equations and Dynamical Systems NEEDS 94, Makhankov et. al. eds, World Scienti c, 1995. Abstract Modulation theory is used to study the Ablowitz-Ladik equations. Exact multiphase wavetrain solutions are found, and local conserva-tion laws are averaged to obtain a macroscopic description of

### Finite-genus solutions for the Hirota s bilinear diﬀerence

to be strange, because usually the ﬁnite-genus solutions naturally appear when one solves quasiperiodic problems. For, example, in 1 + 1 dimensional discrete systems, such as Toda chain, Ablowitz-Ladik equations, etc, the quasiperiodicity leads to the polynomial depen-dence of the scattering matrix of the auxiliary problem on the spectral

### www.researchgate.net

arXiv:nlin/0611055v3 [nlin.SI] 11 Nov 2007 ALGEBRO-GEOMETRIC FINITE-BAND SOLUTIONS OF THE ABLOWITZ LADIK HIERARCHY FRITZ GESZTESY, HELGE HOLDEN, JOHANNA MICHOR, AND GERALD TESCH

### The periodic defocusing Ablowitz Ladik equation and the

applied in the construction of finite genus solutions of a more general version of the AL equation. In particular, the authors in [23] were able to write down the solution of the initial value problem for the periodic defocusing AL equation itself. On the other hand, from a different direction, the

### UMJI - University of Arizona

4 Finite Genus Solutions to the Ablowitz-Ladik Equations 80 Special Classes of Finite Genus Solutions 117 4.3.1 Focusing and Defocusing Solutions. 118

### Institute of Physics

Finite-genus solutions for the Ablowitz-Ladik hierarchy V E Vekslerchik-The Davey - Stewartson equation and the Ablowitz - Ladik hierarchy V E Vekslerchik-The 2D Toda lattice and the Ablowitz-Ladik hierarchy V E Vekslerchik-Recent citations Nonlocal Reductions of the Ablowitz Ladik Equation G. G. Grahovski et al-New integrable differential

### Universal Behavior of Modulationally Unstable Media

scattering transform [61, 62]. Even though certain nonintegrable NLS equations admit solutions that exhibit collapse [52], and even though certain integrable systems admit solutions which blow up in finite time [3, 47], strong numerical and theoretical evidence (see, e.g., [18, 19, 23, 56]) suggests that solutions of the focusing one

### Curriculum Vitae Annalisa Maria Calini (Updated 12-28-2019)

Di erential Equations, Mathematical Sciences Research Institute. Berkeley, CA (01{07/1994) - Research Assistant. University of Arizona (01/1991{12/1993) - Research Associate. Los Alamos National Laboratory (Project with J.C. Scovel and J.M. Hyman on symplectic numerical integrators.) (07{08/1990) - Research Assistant. University of Arizona