Priscila Leal da Silva

A family of wave-breaking equations generalizing the Camassa-Holm and Novikov equations

A 4-parameter polynomial family of equations generalizing the Camassa-Holm and Novikov equations that describe breaking waves is introduced. A classification of low-order conservation laws, peaked travelling wave solutions, and Lie symmetries is presented for this family. These classifications pick out a 1-parameter equation that has several interesting features: it reduces to the Camassa-Holm and Novikov equations when the polynomial has degree two and three; it has a conserved H1 norm and it possesses N-peakon solutions when the polynomial has any degree; and it exhibits wave-breaking for certain solutions describing collisions between peakons and anti-peakons in the case N = 2.

Lie and Noether symmetries for a class of fourth-order Emden?Fowler equations

A group classification of a fourth-order ordinary differential equation is carried out. The Noether symmetries are considered and some first integrals are established. Solutions for special Lane–Emden systems are also obtained from the invariant solutions of the investigated equation.

On the Group Analysis of a Modified Novikov Equation

In this work, we study a modified Novikov equation using group methods. A complete group classification is carried out. Then from the point symmetry generators, we find the one-parameter group of local diffeomorfisms which preserves the equation. From the Lie symmetry generators, we also obtain exact solutions to the considered equation. It is also proved that only one nontrivial conservation law can be established using Ibragimov’s recent developments.

Symmetry analysis of a class of autonomous even-order ordinary differential equations

A class of autonomous, even-order ordinary differential equations is discussed from the point of view of Lie symmetries. It is shown that for a certain power nonlinearity, the Noether symmetry group coincides with the Lie point symmetry group. First integrals are established and exact solutions are found. Furthermore, this paper complements, for the one-dimensional case, some results in the literature of Lie group analysis of poliharmonic equations and Noether symmetries obtained in the last twenty years.

On certain shallow water models, scaling invariance and strict self-adjointness

In this work we establish conditions for a class of third order partial differential equations to be strictly self-adjoint and scale invariant. The obtained family of equations includes the Benjamin-Bona-Mahony, Camassa-Holm and Novikov equations. Using the strict self-adjointness and Ibragimov’s conservation theorem, we establish some local conservation laws for some of the mentioned equations.

Uma nova equação unificando quatro modelos físicos

Neste trabalho deduzimos uma equacao que unica diversos modelos fisicos que de certa forma generaliza resultados recentemente encontrados em [1, 3].

Comparações entre o Teorema de Noether e o Teorema de Ibragimov utilizando uma classe de equações diferenciais ordinárias

Neste trabalho comparamos quantidades conservadas obtidas via Teorema de Noether e Ibragimov. Para tanto, usamos resultados de nossa autoria [I. L. Freire, P. L. da Silva and M. Torrisi, “Lie and Noether symmetries for a class of fourth-orderEmden-Fowler equations”, J. Phys. A: Math Theor., 46(2013)245206] e [ P. L. da Silva and I. L. Freire, “Symmetry analysis of a class of autonomous even-order ordinary differential equations”, arXiv:1311 . 0313 v 1 , (2013)], onde encontramos todas as primeiras integrais obtidas via Teorema de Noether. Em seguida, para a mesma equac¸˜ao, aplicamos os desenvolvimentos propostos por Ibragimov nos u´ltimos 7 anos a fim de encontrar quantidades locais conservadas. Dessa forma, podemos comparar os se resultados obtidos em ambos os casos coincidem ou n˜ao.

Auto-adjunticidade não-linear e leis de conservção da equação de Korteweg-de Vries-Zakharov-Kuznetsov

Neste trabalho apresentaremos condicoes para que a equacao de KdV-ZK seja nao-linearmente auto-adjunta e, assim, utilizaremos o Teorema de Ibragimov para encontrar leis de conservacao dela.