On difference equations concerning Schwarzian equation

Lan, Shuang-Ting; Chen, Zong-Xuan
January 2017
Advances in Difference Equations;1/4/2017, Vol. 2017 Issue 1, p1
Academic Journal
Consider the difference equation where $P(z,f)$ and $Q(z,f)$ are prime polynomials in $f(z)$ with $\deg_{f}P=p, \deg_{f}Q=q$ , and $d=\max\{p,q\}>0$ . We give the supremum of d, an estimation of the sum of Nevanlinna exceptional values of meromorphic solution $f(z)$ of the equation, and study the value distributions of their difference $\Delta f(z)$ and divided difference $\frac{\Delta f(z)}{f(z)}$ .


Related Articles

  • Correspondence between Schwarzian derivative of ODE and cross-ratio of ordinary difference equation. Itoh, Toshiaki // AIP Conference Proceedings;Oct2013, Vol. 1558 Issue 1, p2167 

    Discrete correspondences between Schwarzian derivative and Cross-ratio are treated numerically. It is hard to construct discrete version of Schwarzian derivative from its continuous form in ODE theory directly. Instead, it found we can use the same strategy for the solutions of ordinary...

  • Reciprocal Bäcklund transformations of autonomous evolution equations. Euler, M.; Euler, N.; Lundberg, S. // Theoretical & Mathematical Physics;Jun2009, Vol. 159 Issue 3, p770 

    We discuss the construction of reciprocal Bäcklund transformations for evolution equations using integrating factors of zeroth and higher orders with their corresponding conservation laws. As an example, we consider the Harry Dym equation and the Schwarzian KdV equation.

  • Puzzles, Challenges and Investigations.  // Teaching Mathematics & its Applications;1997, Vol. 16 Issue 1, p46 

    A quiz concerning different mathematical problems and equation, is presented.

  • Generalized Cauchy matrix approach for lattice Boussinesq-type equations. Zhao, Songlin; Zhang, Dajun; Shi, Ying // Chinese Annals of Mathematics;Mar2012, Vol. 33 Issue 2, p259 

    The authors generalize the Cauchy matrix approach to get exact solutions to the lattice Boussinesq-type equations: lattice Boussinesq equation, lattice modified Boussinesq equation and lattice Schwarzian Boussinesq equation. Some kinds of solutions including soliton solutions, Jordan block...

  • Conservation laws of some lattice equations. Cheng, Junwei; Zhang, Dajun // Frontiers of Mathematics in China;Oct2013, Vol. 8 Issue 5, p1001 

    We derive infinitely many conservation laws for some multidimensionally consistent lattice equations from their Lax pairs. These lattice equations are the Nijhoff-Quispel-Capel equation, lattice Boussinesq equation, lattice nonlinear Schrödinger equation, modified lattice Boussinesq equation,...

  • Second-order recursion operators of third-order evolution equations with fourth-order integrating factors. Euler, Marianna; Euler, Norbert // Journal of Nonlinear Mathematical Physics (Atlantis Press);Oct2007, Vol. 14 Issue 3, p313 

    We report the recursion operators for a class of symmetry integrable evolution equations of third order which admit a fourth-order integrating factor. Under some as-sumptions we obtain the complete list of equations, one of which is a special case of the Schwarzian Korteweg-de Vries equation.

  • Isomonodromic flows for Fuchsian connections on Riemann surfaces. Pinchbeck, David J. // IMRN: International Mathematics Research Notices;2005, Vol. 2005 Issue 40, p2473 

    A Schlesinger-Teichmüller Hamiltonian structure is described for isomonodromic deformations of Fuchsian connections and Schwarzian equations of second order on Riemann surfaces as the underlying surface varies in Teichmüller space.

  • On the monodromy group for the super Schwarzian differential equation. Uehara, Shozo; Yasui, Yukinori // Journal of Mathematical Physics;Nov91, Vol. 32 Issue 11, p2972 

    The first variation of the monodromy group associated with a super Schwarzian differential equation is calculated. The relation between the monodromy period and the Fenchel–Nielsen deformation of a super Riemann surface is presented.

  • A Modified Schwarzian Korteweg–de Vries Equation in 2 + 1 Dimensions with Lots of Isochronous Solutions. Calogero, F.; Mariani, M. // Physics of Atomic Nuclei;Oct2005, Vol. 68 Issue 10, p1646 

    A modified version of the integrable Schwarzian Korteweg de Vries equation in 2 + 1 dimensions is introduced, and it is pointed out that it possesses lots of isochronous solutions.© 2005 Pleiades Publishing, Inc.

  • New solutions of the Schwarzian Korteweg-de Vries equation in 2+1 dimensions based on weak symmetries. Gandarias, M.; Bruz�n, M. // Theoretical & Mathematical Physics;Jun2007, Vol. 151 Issue 3, p752 

    We consider the (2+1)-dimensional integrable Schwarzian Korteweg-de Vries equation. Using weak symmetries, we obtain a system of partial differential equations in 1+1 dimensions. Further reductions lead to second-order ordinary differential equations that provide new solutions expressible in...


Read the Article


Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics