American Institute of Mathematical Sciences

Advanced
August  2010, 27(3): 1233-1239. doi: 10.3934/dcds.2010.27.1233

On the spatial asymptotics of solutions of the Toda lattice

Gerald Teschl 1,

1. 

Faculty of Mathematics, University of Vienna, Nordbergstrasse 15, 1090 Wien

Received  June 2009 Revised  January 2010 Published  March 2010

We investigate the spatial asymptotics of decaying solutions of the Toda hierarchy and show that the asymptotic behaviour is preserved by the time evolution. In particular, we show that the leading asymptotic term is time independent. Moreover, we establish infinite propagation speed for the Toda lattice.
Keywords: Toda hierarchy, Toda lattice, spatial asymptotics, Kac-van Moerbeke hierarchy..
Mathematics Subject Classification: Primary 37K40, 37K15; Secondary 35Q53, 37K1.
Citation: Gerald Teschl. On the spatial asymptotics of solutions of the Toda lattice. Discrete & Continuous Dynamical Systems - A, 2010, 27 (3) : 1233-1239. doi: 10.3934/dcds.2010.27.1233
[1]

Isaac Alvarez-Romero, Gerald Teschl. On uniqueness properties of solutions of the Toda and Kac-van Moerbeke hierarchies. Discrete & Continuous Dynamical Systems - A, 2017, 37 (5) : 2259-2264. doi: 10.3934/dcds.2017098
[2]

Carlos Tomei. The Toda lattice, old and new. Journal of Geometric Mechanics, 2013, 5 (4) : 511-530. doi: 10.3934/jgm.2013.5.511
[3]

Andreas Henrici. Symmetries of the periodic Toda lattice, with an application to normal forms and perturbations of the lattice with Dirichlet boundary conditions. Discrete & Continuous Dynamical Systems - A, 2015, 35 (7) : 2949-2977. doi: 10.3934/dcds.2015.35.2949
[4]

Avner Friedman. A hierarchy of cancer models and their mathematical challenges. Discrete & Continuous Dynamical Systems - B, 2004, 4 (1) : 147-159. doi: 10.3934/dcdsb.2004.4.147
[5]

Yong Liu. Even solutions of the Toda system with prescribed asymptotic behavior. Communications on Pure & Applied Analysis, 2011, 10 (6) : 1779-1790. doi: 10.3934/cpaa.2011.10.1779
[6]

Manuel del Pino, Michal Kowalczyk, Juncheng Wei. The Jacobi-Toda system and foliated interfaces. Discrete & Continuous Dynamical Systems - A, 2010, 28 (3) : 975-1006. doi: 10.3934/dcds.2010.28.975
[7]

Kazuo Aoki, Pierre Charrier, Pierre Degond. A hierarchy of models related to nanoflows and surface diffusion. Kinetic & Related Models, 2011, 4 (1) : 53-85. doi: 10.3934/krm.2011.4.53
[8]

Isabelle Choquet, Pierre Degond, Brigitte Lucquin-Desreux. A hierarchy of diffusion models for partially ionized plasmas. Discrete & Continuous Dynamical Systems - B, 2007, 8 (4) : 735-772. doi: 10.3934/dcdsb.2007.8.735
[9]

Daniel T. Wise. Research announcement: The structure of groups with a quasiconvex hierarchy. Electronic Research Announcements, 2009, 16: 44-55. doi: 10.3934/era.2009.16.44
[10]

Vladimir S. Gerdjikov, Georgi Grahovski, Rossen Ivanov. On the integrability of KdV hierarchy with self-consistent sources. Communications on Pure & Applied Analysis, 2012, 11 (4) : 1439-1452. doi: 10.3934/cpaa.2012.11.1439
[11]

Zhuchun Li. Effectual leadership in flocks with hierarchy and individual preference. Discrete & Continuous Dynamical Systems - A, 2014, 34 (9) : 3683-3702. doi: 10.3934/dcds.2014.34.3683
[12]

Rossen I. Ivanov. Conformal and Geometric Properties of the Camassa-Holm Hierarchy. Discrete & Continuous Dynamical Systems - A, 2007, 19 (3) : 545-554. doi: 10.3934/dcds.2007.19.545
[13]

Iryna Egorova, Johanna Michor, Gerald Teschl. Rarefaction waves for the Toda equation via nonlinear steepest descent. Discrete & Continuous Dynamical Systems - A, 2018, 38 (4) : 2007-2028. doi: 10.3934/dcds.2018081
[14]

Weiwei Ao. Sharp estimates for fully bubbling solutions of $B_2$ Toda system. Discrete & Continuous Dynamical Systems - A, 2016, 36 (4) : 1759-1788. doi: 10.3934/dcds.2016.36.1759
[15]

Fritz Gesztesy, Helge Holden, Johanna Michor, Gerald Teschl. The algebro-geometric initial value problem for the Ablowitz-Ladik hierarchy. Discrete & Continuous Dynamical Systems - A, 2010, 26 (1) : 151-196. doi: 10.3934/dcds.2010.26.151
[16]

Anahita Eslami Rad, Enrique G. Reyes. The Kadomtsev-Petviashvili hierarchy and the Mulase factorization of formal Lie groups. Journal of Geometric Mechanics, 2013, 5 (3) : 345-364. doi: 10.3934/jgm.2013.5.345
[17]

Paul Fife, Joseph Klewicki, Tie Wei. Time averaging in turbulence settings may reveal an infinite hierarchy of length scales. Discrete & Continuous Dynamical Systems - A, 2009, 24 (3) : 781-807. doi: 10.3934/dcds.2009.24.781
[18]

Nancy López Reyes, Luis E. Benítez Babilonia. A discrete hierarchy of double bracket equations and a class of negative power series. Mathematical Control & Related Fields, 2017, 7 (1) : 41-52. doi: 10.3934/mcrf.2017003
[19]

Wendai Lv, Siping Ji. Atmospheric environmental quality assessment method based on analytic hierarchy process. Discrete & Continuous Dynamical Systems - S, 2019, 12 (4&5) : 941-955. doi: 10.3934/dcdss.2019063
[20]

Juncheng Wei, Jun Yang. Toda system and interior clustering line concentration for a singularly perturbed Neumann problem in two dimensional domain. Discrete & Continuous Dynamical Systems - A, 2008, 22 (3) : 465-508. doi: 10.3934/dcds.2008.22.465

2018 Impact Factor: 1.143

Tools

Metrics

  • PDF downloads (10)
  • HTML views (0)
  • Cited by (4)

Other articles
by authors

[Back to Top]

Copyright © 2019 American Institute of Mathematical Sciences