Symmetry Reduction and Soliton-Like Solutions for the Generalized Korteweg-De Vries Equation
- Authors: Blázquez-Sanz D.1, Conde Martín J.M.2
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Affiliations:
- Universidad Nacional de Colombia
- Universidad San Francisco de Quito
- Issue: Vol 39, No 9 (2018)
- Pages: 1305-1314
- Section: Part 2. Special issue “Actual Problems of Algebra and Analysis” Editors: A. M. Elizarov and E. K. Lipachev
- URL: https://journals.rcsi.science/1995-0802/article/view/203247
- DOI: https://doi.org/10.1134/S1995080218090366
- ID: 203247
Cite item
Abstract
We analyze the gKdV equation, a generalized version of Korteweg-de Vries with an arbitrary function f(u). In general, for a function f(u) the Lie algebra of symmetries of gKdV is the 2-dimensional Lie algebra of translations of the plane xt. This implies the existence of plane wave solutions. Indeed, for some specific values of f(u) the equation gKdV admits a Lie algebra of symmetries of dimension grater than 2. We compute the similarity reductions corresponding to these exceptional symmetries. We prove that the gKdV equation has soliton-like solutions under some general assumptions, and we find a closed formula for the plane wave solutions, that are of hyperbolic secant type.
About the authors
D. Blázquez-Sanz
Universidad Nacional de Colombia
Author for correspondence.
Email: dblazquezs@unal.edu.co
Colombia, Sede Medellín
J. M. Conde Martín
Universidad San Francisco de Quito
Email: dblazquezs@unal.edu.co
Ecuador, Quito