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Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA


Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania


Group Analysis of the Generalized Hunter-Saxton System

Discontinuity, Nonlinearity, and Complexity 6(2) (2017) 165--171 | 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, 13083-859, Campinas/SP, Brasil

$^{2}$ Instituto Federal de Educação, Ciência e Tecnologia de São Paulo - IFSP, Acesso Dr. João Batista Merlin, s/no, Jardim Itália, 13872-551 - São João da Boa Vista - SP, Brasil

$^{3}$ Instituto de Física “Gleb Wataghin” - IFGW, Universidade Estadual de Campinas - UNICAMP, 13083-859 - Campinas - SP, Brasil

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We find the Lie point symmetries of the generalized two-component Hunter-Saxton system. Then we show that it is nonlinearly self-adjoint 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.


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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