# Nonlinear Dynamics of Moving Curves and Surfaces: Applications to Physical Systems

@article{Murugesh2004NonlinearDO, title={Nonlinear Dynamics of Moving Curves and Surfaces: Applications to Physical Systems}, author={S. Murugesh and Muthusamy Lakshmanan}, journal={Int. J. Bifurc. Chaos}, year={2004}, volume={15}, pages={51-63} }

The subject of moving curves (and surfaces) in three-dimensional space (3-D) is a fascinating topic not only because it represents typical nonlinear dynamical systems in classical mechanics, but also finds important applications in a variety of physical problems in different disciplines. Making use of the underlying geometry, one can very often relate the associated evolution equations to many interesting nonlinear evolution equations, including soliton possessing nonlinear dynamical systems…

## 11 Citations

### Motion of Space Curves in Three-dimensional Minkowski Space $R_1^{3}$, SO(2,1) Spin Equation and Defocusing Nonlinear Schr\

- Mathematics, Physics
- 2010

We consider the dynamics of moving curves in three-dimensional Minkowski space and deduce the evolution equations for the curvature and torsion of the curve. Next by mapping a continuous SO(2,1)…

### Knot soliton solutions for the one-dimensional non-linear Schrödinger equation

- Mathematics, PhysicsJournal of Physics Communications
- 2018

We identify that a breather soliton solution for the one-dimensional non-linear Schrödinger equation, presented here, is characteristically distinct when one studies the associated space curve,…

### An Inhomogeneous Space–Time Patching Model Based on a Nonlocal and Nonlinear Schrödinger Equation

- Mathematics
- 2016

We consider an integrable, nonlocal and nonlinear, Schrödinger equation (NNSE) as a model for building space–time patchings in inhomogeneous loop quantum cosmology (LQC). We briefly review exact…

### Rogue waves and breathers in Heisenberg spin chain

- Physics
- 2015

Abstract
Following the connection of the non-linear Schrödinger equation with the continuum Heisenberg spin chain, we find the rogue soliton equivalent in the spin system. The breathers are also…

### Notes on dispersionful and dispersionless vortex filament equations in 1+1 and 2+1 dimensions

- Physics
- 2004

The vortex filament equations (VFE) in 1+1 and 2+1 dimensions are considered. Some of these equations are integrable. Also the VFE with potentials and with self-consistent potentials are presented.…

### Exact and non-exact Fermi–Pasta–Ulam–Tsingou recurrences in a Heisenberg ferromagnet

- PhysicsPhysica Scripta
- 2020

We visualize the Fermi–Pasta–Ulam–Tsingou (FPUT) recurrence in a classical Heisenberg ferromagnetic (HF) spin chain by exploiting its gauge equivalence to the nonlinear Schrödinger equation (NLSE).…

### Anholonomy according to three formulations of non-null curve evolution

- Mathematics
- 2017

In this paper, we present three anholonomy densities and three geometric phases for three formulations of curve evolution in Minkowski 3-space and give applications of three formulation for…

### Measurement Properties of Simple Biomechanical Measures of Walking Effort

- Biology, Engineering
- 2009

Four biomechanical walking effort outcomes are presented that have good theoretical underpinnings, excellent reproducibility and responsiveness, are simple and easy to administer with relatively inexpensive equipment, and can be used in real world environments.

### Three classes of non-lightlike curve evolution according to Darboux frame and geometric phase

- Mathematics
- 2017

In this paper, we present three classes of non-lightlike curve evolution according to the Darboux frame and we give three geometric phases according to three classes in Minkowski 3-space.

### The Impact of ICTs Diffusion on MDGs and Baroclinic Digital Learning Environments in East and Southern Africa

- Economics
- 2012

The paper proved the correlation and potential application of Chaos Theory to the design model for digital learning environments and explored the emerging trends in E-learning from ICTs for development.

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