Soliton surfaces associated with sigma models: differential and algebraic aspects
PP Goldstein, AM Grundland… - Journal of Physics A …, 2012 - iopscience.iop.org
Soliton surfaces associated with sigma models: differential and algebraic aspects - IOPscience
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Soliton surfaces and generalized symmetries of integrable systems
AM Grundland, S Post, D Riglioni - Journal of Physics A …, 2013 - iopscience.iop.org
In this paper, we discuss some specific features of symmetries of integrable systems which
can be used to construct the Fokas–Gel'fand formula for the immersion of 2D-soliton …
can be used to construct the Fokas–Gel'fand formula for the immersion of 2D-soliton …
Surfaces immersed in Lie algebras associated with elliptic integrals
AM Grundland, S Post - Journal of Physics A: Mathematical and …, 2011 - iopscience.iop.org
The objective of this work is to adapt the Fokas–Gel'fand immersion formula to ordinary
differential equations written in the Lax representation. The formalism of generalized vector …
differential equations written in the Lax representation. The formalism of generalized vector …
On a stack of surfaces obtained from the sigma models
PP Goldstein, AM Grundland - arxiv preprint arxiv:1710.01642, 2017 - arxiv.org
Under the assumption that the $\mathbb {C} P^{N-1} $ sigma model is defined on the
Riemann sphere and its action functional is finite, we derive surfaces induced by surfaces …
Riemann sphere and its action functional is finite, we derive surfaces induced by surfaces …
Soliton surfaces in the generalized symmetry approach
AM Grundland - Theoretical and Mathematical Physics, 2016 - Springer
We investigate some features of generalized symmetries of integrable systems aiming to
obtain the Fokas–Gel'fand formula for the immersion of two-dimensional soliton surfaces in …
obtain the Fokas–Gel'fand formula for the immersion of two-dimensional soliton surfaces in …
On immersion formulas for soliton surfaces
This paper is devoted to a study of the connections between three different analytic
descriptions for the immersion functions of 2D-surfaces corresponding to the following three …
descriptions for the immersion functions of 2D-surfaces corresponding to the following three …
Soliton surfaces via a zero-curvature representation of differential equations
AM Grundland, S Post - Journal of Physics A: Mathematical and …, 2012 - iopscience.iop.org
The main aim of this paper is to introduce a new version of the Fokas–Gel'fand formula for
immersion of soliton surfaces in Lie algebras. The paper contains a detailed exposition of …
immersion of soliton surfaces in Lie algebras. The paper contains a detailed exposition of …
Supersymmetric versions of the Fokas–Gel'fand formula for immersion
S Bertrand, AM Grundland - Journal of Physics A: Mathematical …, 2016 - iopscience.iop.org
In this paper, we construct and investigate two supersymmetric versions of the Fokas–
Gel'fand formula for the immersion of 2D surfaces associated with a supersymmetric …
Gel'fand formula for the immersion of 2D surfaces associated with a supersymmetric …
Soliton surfaces associated with ℂPN− 1 sigma models
AM Grundland, S Post - Journal of Physics: Conference Series, 2012 - iopscience.iop.org
Soliton surfaces associated with the Bbb CPN− 1 sigma model are constructed using the
Generalized Weierstrass and the Fokas-Gel'fand formulas for immersion of 2D surfaces in …
Generalized Weierstrass and the Fokas-Gel'fand formulas for immersion of 2D surfaces in …
Minimal surfaces in the soliton surface approach
A Doliwa, AM Grundland - arxiv preprint arxiv:1511.02173, 2015 - arxiv.org
The main objective of this paper is to derive the Enneper-Weierstrass representation of
minimal surfaces in $\mathbb {E}^ 3$ using the soliton surface approach. We exploit the …
minimal surfaces in $\mathbb {E}^ 3$ using the soliton surface approach. We exploit the …