27 citations · 112 across the 27 of their papers we have counts for
23 papers
On Riemann wave superpositions obtained from the Euler system
Łukasz Chomienia, Alfred Michel Grundland
The paper contains an analysis of the conditions for the existence of elastic versus non-elastic wave superpositions governed by the Euler system in (1+1)-dimensions. A review of r…
Nonlinear wave superpositions and quasi-rectifiable Lie modules
Łukasz Chomienia, Alfred Michel Grundland
This paper presents a study of nonlinear superpositions of Riemann wave solutions admitted by quasilinear hyperbolic first-order systems of partial differential equations. In parti…
Stability analysis of the -dimensional Nambu-Goto action gas models
Alfred M. Grundland, Javier de Lucas, Bartosz M. Zawora
The aim of this paper is to perform a nonlinear stability analysis of the -dimensional Nambu-Goto action gas models. The energy-Casimir method is employed to discuss in deta…
A purely analytic derivation of Bonnet surfaces
Robert Conte, A. Michel Grundland
Bonnet has characterized his surfaces by a geometric condition. What is done here is a characterization of the same surfaces by two analytic conditions: (i) the mean curvature …
Quasi-rectifiable Lie algebras for partial differential equations
A. M. Grundland, J. de Lucas
We introduce families of quasi-rectifiable vector fields and study their geometric and algebraic aspects. Then, we analyse their applications to systems of partial differential equ…
The Lie algebra of the lowest transitively differential group of degree three
Alfred Michel Grundland, Ian Marquette
We investigate the real Lie algebra of first-order differential operators with polynomial coefficients, which is subject to the following requirements. (1) The Lie algebra should a…