### Abstract

Original language | English |
---|---|

Pages (from-to) | 167-175 |

Number of pages | 9 |

Journal | Molecular Crystals and Liquid Crystals |

Volume | 525 |

DOIs | |

Publication status | Published - 13 Jul 2010 |

Event | 10th European Conference on Liquid Crystals (ECLC 2009) - Colmar, France Duration: 19 Apr 2009 → 24 Apr 2009 |

### Fingerprint

### Keywords

- smectic C*
- soliton
- wave speed

### Cite this

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*Molecular Crystals and Liquid Crystals*, vol. 525, pp. 167-175. https://doi.org/10.1080/15421401003799243

**Computing the wave speed of soliton-like solutions in SmC* liquid crystals.** / Seddon, Lawrence; Stewart, Iain W.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Computing the wave speed of soliton-like solutions in SmC* liquid crystals

AU - Seddon, Lawrence

AU - Stewart, Iain W.

PY - 2010/7/13

Y1 - 2010/7/13

N2 - We present a novel method for numerically computing the wave speed of a soliton-like travelling wave in chiral smectic C liquid crystals (SmC*) that satisfies a parabolic partial differential equation (PDE) with a general nonlinear term [1]. By transforming the PDE to a co-moving frame and recasting the resulting problem in phase-space, the original PDE can be expressed as an integral equation known as an exceptional nonlinear Volterra-type equation of the second kind. This technique is motivated by, but distinct in nature from, iterative integral methods introduced by Chernyak [2]. By applying a simple trapezoidal method to the integral equation we generate a system of nonlinear simultaneous equations which we solve for our phase plane variable at equally spaced intervals using Newton iterates. The equally spaced phase variable solutions are then used to compute the wave speed of the associated travelling wave. We demonstrate an algorithm for performing the necessary calculations by considering an example from liquid crystal theory, where a parabolic PDE with a nonlinear reaction term has a solution and wave speed which are known exactly [3,4]. The analytically derived wave speed is then compared with the numerically computed wave speed using our new scheme.

AB - We present a novel method for numerically computing the wave speed of a soliton-like travelling wave in chiral smectic C liquid crystals (SmC*) that satisfies a parabolic partial differential equation (PDE) with a general nonlinear term [1]. By transforming the PDE to a co-moving frame and recasting the resulting problem in phase-space, the original PDE can be expressed as an integral equation known as an exceptional nonlinear Volterra-type equation of the second kind. This technique is motivated by, but distinct in nature from, iterative integral methods introduced by Chernyak [2]. By applying a simple trapezoidal method to the integral equation we generate a system of nonlinear simultaneous equations which we solve for our phase plane variable at equally spaced intervals using Newton iterates. The equally spaced phase variable solutions are then used to compute the wave speed of the associated travelling wave. We demonstrate an algorithm for performing the necessary calculations by considering an example from liquid crystal theory, where a parabolic PDE with a nonlinear reaction term has a solution and wave speed which are known exactly [3,4]. The analytically derived wave speed is then compared with the numerically computed wave speed using our new scheme.

KW - smectic C

KW - soliton

KW - wave speed

U2 - 10.1080/15421401003799243

DO - 10.1080/15421401003799243

M3 - Article

VL - 525

SP - 167

EP - 175

JO - Molecular Crystals and Liquid Crystals

JF - Molecular Crystals and Liquid Crystals

SN - 1542-1406

ER -