Pseudo-potentials, nonlocal symmetries and integrability of some shallow water equations

2002/12/19 by Enrique G. Reyes, Reyes, Enrique G. · 1 citation
Mathematics · Physics and Astronomy · #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Mathematical Physics (math-ph) #Pattern Formation and Solitons (nlin.PS) #math-ph #math.MP #nlin.PS #nlin.SI

paper · pdf · doi:10.48550/arxiv.nlin/0212045

31 pages

arxiv created 2002/12/19 · arxiv updated 2009/11/30

Abstract

Zero curvature formulations, pseudo-potentials, modified versions, ``Miura transformations'', and nonlocal symmetries of the Korteweg--de Vries, Camassa-- Holm and Hunter--Saxton equations are investigated from an unified point of view: these three equations belong to a two--parameters family of equations ``describing pseudo-spherical surfaces'', and therefore their basic integrability properties can be studied by geometrical means.

Cited by

• On a class of third order differential equations describing pseudospherical or spherical surfaces

Related

• Pseudo-potentials and local isometric immersion for a generalized Camassa-Holm equation describing pseudospherical surfaces
• Nonlocal symmetry, Darboux transformation and soliton-cnoidal wave interaction solution for the shallow water wave equation
• Nonlocal symmetries and exact solutions of the (2+1)-dimensional generalised variable coefficient shallow water wave equation
• Shallow Water Wave Systems
• Local Isometric immersions of pseudo-spherical surfaces and evolution equations