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Symmetries for a family of Boussinesq equations with nonlinear dispersion

✍ Scribed by M.S. Bruzón; M.L. Gandarias

Publisher
Elsevier Science
Year
2009
Tongue
English
Weight
976 KB
Volume
14
Category
Article
ISSN
1007-5704

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✦ Synopsis

In this paper, we make a full analysis of a family of Boussinesq equations which include nonlinear dispersion by using the classical Lie method of infinitesimals. We consider travelling wave reductions and we present some explicit solutions: solitons and compactons.

For this family, we derive nonclassical and potential symmetries. We prove that the nonclassical method applied to these equations leads to new symmetries, which cannot be obtained by Lie classical method. We write the equations in a conserved form and we obtain a new class of nonlocal symmetries. We also obtain some Type-II hidden symmetries of a Boussinesq equation.

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