Wesley B. Cardoso,1 Luca Salasnich,2, 3 and Boris A. Malomed4, 5 1Instituto de Fı́sica, Universidade Federal de Goiás, 74.690-900, Goiânia, Goiás, Brazil 2Dipartimento di Fisica e Astronomia “Galileo Galilei” and CNISM, Università di Padova, Via Marzolo 8, 35131 Padova, Italy 3Istituto Nazionale di Ottica (INO) del Consiglio Nazionale delle Ricerche (CNR), Sezione di Sesto Fiorentino, Via Nello ...

The conditions for a generalized Burgers equation which a priori involves nine arbitrary functions of one, or two variables to allow an infinite dimensional symmetry algebra are determined. Though this algebra can involve up to two arbitrary functions of time, it does not allow a Virasoro algebra. This result confirms that variable coefficient generalizations of a non-integrable equation should...

the main purpose of this article is to present an approximate solution for the two-dimensional nonlinear volterra integral equations using legendre orthogonal polynomials. first, the two-dimensional shifted legendre orthogonal polynomials are defined and the properties of these polynomials are presented. the operational matrix of integration and the product operational matrix are introduced. th...

in this paper we consider a nonlinear two-phase stefan problem in one-dimensional space. the problem is mapped into a nonlinear volterra integral equation for the free boundary.