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New exact solutions are obtained for several nonlinear physical equations, namely the Navier–Stokes and Euler systems, an isentropic compressible fluid system and a vector nonlinear Schrödinger… (More)

We present a version of the conditional symmetry method in order to obtain multiple wave solutions expressed in terms of Riemann invariants. We construct an abelian distribution of vector fields… (More)

- Alfred Michel Grundland, A. Strasburger, Wojtek J. Zakrzewski
- 2005

We study some geometrical aspects of two dimensional orientable surfaces arrising from the study of CP N sigma models. To this aim we employ an identification of R N (N +2) with the Lie algebra su (N… (More)

- R. Conte, Alfred Michel Grundland, Micheline Musette
- 2006

Among the reductions of the resonant three-wave interaction system to six-dimensional differential systems , one of them has been specifically mentioned as being linked to the generic sixth Painlevé… (More)

- E. V. FERAPONTOV, Alfred Michel Grundland, E. V. Ferapontov, Alfred Michel Grundland
- 2000

Transformations between different analytic descriptions of constant mean curvature (CMC) surfaces are established. In particular, it is demonstrated that the system ∂ψ 1 = (|ψ 1 | 2 + |ψ 2 | 2)ψ 2 ¯… (More)

- Alfred Michel Grundland, Alexander J. Hariton, L. Šnobl
- 2009

A comprehensive symmetry analysis of the N = 1 supersymmetric sine–Gordon equation is performed. Two different forms of the supersymmetric system are considered. We begin by studying a system of… (More)

Analysis of the generalized Weierstrass-Enneper system includes the estimation of the degree of indeterminancy of the general analytic solution and the discussion of the boundary value problem.… (More)

In this paper we study certain aspects of the complete integrability of the Generalized Weierstrass system in the context of the Sinh-Gordon type equation. Using the conditional symmetry approach, we… (More)

- Alfred Michel Grundland, Willy Hereman, İ. Yurduşen
- 2008

Two-dimensional conformally parametrized surfaces immersed in the su(N) algebra are investigated. The focus is on surfaces parametrized by solutions of the equations for the CP N−1 sigma model. The… (More)

In this paper we employ a ”direct method” in order to obtain rank-k solutions of any hyperbolic system of first order quasilinear differential equations in many dimensions. We discuss in detail the… (More)