| Abstract: |
| Since the breakthrough discovery of properties of the Camassa-Holm equation, intense research has been dedicated to the study of third order non-locally evolutive partial differential equations. In terms of solutions, one classical approach is the determination of quadratures to analyse zeros os polynomials to obtain explicit solutions. However, the majority of non-linear equations fails to admit quadratures and the study of solutions becomes almost an impossible task. In this talk we will discuss a family of non-locally evolutive equations and show that although singularities arrise, it is possible to impose some weak assumptions over its solutions and make use of its conservation laws to classify the existence of bounded traveling wave solutions. |
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