## Proceedings of the International Conference on Geometry, Integrability and Quantization

### Surfaces From Deformation of Parameters

#### Abstract

We construct surfaces from modified Korteweg-de Vries (mKdV) and sine-Gordon (SG) soliton solutions by the use of parametric deformations. For each case there are two types of deformations. The first one gives surfaces on spheres and the second one gives highly complicated surfaces in three dimensional Euclidean space (${\mathbb R}^3$). The SG surfaces that we obtained are not the critical points of functional where the Lagrange function is a polynomial function of the Gaussian ($K$) and mean ($H$) curvatures of the surfaces. We also give the graph of interesting mKdV and SG surfaces arise from parametric deformations.

#### Article information

Dates
First available in Project Euclid: 15 December 2015

Permanent link to this document
https://projecteuclid.org/ euclid.pgiq/1450194166

Digital Object Identifier
doi:10.7546/giq-17-2016-318-343

Mathematical Reviews number (MathSciNet)
MR3445439

Zentralblatt MATH identifier
1384.53004

#### Citation

Tek, Süleyman; Gürses, Metin. Surfaces From Deformation of Parameters. Proceedings of the Seventeenth International Conference on Geometry, Integrability and Quantization, 318--343, Avangard Prima, Sofia, Bulgaria, 2016. doi:10.7546/giq-17-2016-318-343. https://projecteuclid.org/euclid.pgiq/1450194166