Discontinuity, Nonlinearity, and Complexity
Group Analysis of the Generalized HunterSaxton System
Discontinuity, Nonlinearity, and Complexity 6(2) (2017) 165171  DOI:10.5890/DNC.2017.06.004
Yuri Bozhkov$^{1}$, Valter Aparecido Silva Junior$^{2}$,$^{3}$
$^{1}$ Instituto de Matemática, Estatística e Computação Científica  IMECC, Universidade Estadual de Campinas  UNICAMP, 13083859, Campinas/SP, Brasil
$^{2}$ Instituto Federal de Educação, Ciência e Tecnologia de São Paulo  IFSP, Acesso Dr. João Batista Merlin, s/no, Jardim Itália, 13872551  São João da Boa Vista  SP, Brasil
$^{3}$ Instituto de Física “Gleb Wataghin”  IFGW, Universidade Estadual de Campinas  UNICAMP, 13083859  Campinas  SP, Brasil
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Abstract
We find the Lie point symmetries of the generalized twocomponent HunterSaxton system. Then we show that it is nonlinearly selfadjoint and establish the corresponding conservation laws using a recent theorem of Nail Ibragimov which enables one to determine conservation laws for problems without variational structure. Finally we obtain some invariant solutions.
Acknowledgments
We wish to thank Professor Nail Ibragimov for his useful comments on this work as well as for his firm encouragement. Yuri Bozhkov would also like to thank FAPESP, São Paulo, Brasil, for financial support.
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