Open Access. Powered by Scholars. Published by Universities.®
- Keyword
-
- Higher order Hirota equation; Embedded solitons; Soliton perturbation theory; Solitary wave tails (1)
- Mathematical modelling (1)
- Nonlinear optics (1)
- Solitons and modulation theory (1)
- The dual reciprocity boundary element method (DRBEM); Nonlinear Boussinesq equations; Wave diffraction and refraction (1)
Articles 1 - 3 of 3
Full-Text Articles in Physics
Soliton Perturbation Theory For A Higher-Order Hirota Equation, Tim Marchant
Soliton Perturbation Theory For A Higher-Order Hirota Equation, Tim Marchant
Tim Marchant
Solitary wave evolution for a higher order Hirota equation is examined. For the higher order Hirota equation resonance between the solitary waves and linear radiation causes radiation loss. Soliton perturbation theory is used to determine the details of the evolving wave and its tail. An analytical expression for the solitary wave tail is derived and compared to numerical solutions. An excellent comparison between numerical and theoretical solutions is obtained for both right- and left-moving waves. Also, a two-parameter family of higher order asymptotic embedded solitons is identified.
Modulation Analysis Of Boundary Induced Motion Of Optical Solitary Waves In A Nematic Liquid Crystal, Tim Marchant
Modulation Analysis Of Boundary Induced Motion Of Optical Solitary Waves In A Nematic Liquid Crystal, Tim Marchant
Tim Marchant
We consider the motion of a solitary wave, a nematicon, in a finite cell filled with a nematic liquid crystal. A modulation theory is developed to describe the boundary-induced bouncing of a nematicon in a one-dimensional cell and it is found to give predictions in very good agreement with numerical solutions. The boundary-induced motion is then considered numerically for a two-dimensional cell and a simple extension of the modulation theory from one to two space dimensions is then made, with good agreement being found with numerical solutions for the nematicon trajectory. The role of nematicon shape and relative position to …
A Perturbation Drbem Model For Weakly Nonlinear Wave Run-Ups Around Islands, Tim Marchant
A Perturbation Drbem Model For Weakly Nonlinear Wave Run-Ups Around Islands, Tim Marchant
Tim Marchant
In this paper, the dual reciprocity boundary element method (DRBEM) based on the perturbation method is presented for calculating run-ups of weakly nonlinear long waves scattered by islands. Under the assumption that the incident waves are harmonic, the time-dependent nonlinear Boussinesq equations are transformed into three time-independent linear equations by using the perturbation method, where, besides nonlinearity ε, the dispersion μ2 is also included in the perturbed expansion. The first-order solution η0 is found by using the linear long-wave equations. Then η0 is used in two second-order governing equations related to the dispersion and nonlinearity, respectively. Since no any omission …