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Soliton interactions for the extended Korteweg-de Vries (KdV) equation are examined. It is shown that the extended KdV equation can be transformed (to its order of approximation) to a higher-order member of the KdV hierarchy of integrable equations. This transformation is used to derive the higher-order, two-soliton solution for the extended KdV equation.… (More)

- T. R. Marchant
- Physical review. E, Statistical, nonlinear, and…
- 2002

Solitary wave interaction for a higher-order modified Korteweg-de Vries (mKdV) equation is examined. The higher-order mKdV equation can be asymptotically transformed to the mKdV equation, if the higher-order coefficients satisfy a certain algebraic relationship. The transformation is used to derive the higher-order two-soliton solution and it is shown that… (More)

- T. R. Marchant
- 2002

The interaction of solitary waves on shallow water is examined to fourth order. At first order the interaction is governed by the Korteweg–de Vries (KdV) equation, and it is shown that the unidirectional assumption, of right-moving waves only, is incompatible with mass conservation at third order. To resolve this, a mass conserving system of KdV equations,… (More)

Optical spatial solitary waves are considered in a nonlocal thermal focusing medium with non-symmetric boundary conditions. The governing equations consist of a nonlinear Schrödinger equation for the light beam and a Poisson equation for the temperature of the medium. Three numerical methods are investigated for calculating the ground and excited solitary… (More)

- William C. Mann, T. R. Marchant, Minoru Tomita, L F Fraas, Katherine Stanton
- Care management journals : Journal of case…
- 2001

This study examined frail elders' acceptance of the concept of home monitoring devices. With the potential of such devices to ultimately assist many older persons, acceptance of the device in the individual's home is a critical component. Elders who view devices negatively--as unnecessary, unattractive, or intrusive--may be less likely to use the device if… (More)

- By T. R. Marchant, T. R. Marchant
- 2002

The Gray–Scott model of cubic-autocatalysis with linear decay is coupled with diffusion and considered in a one-dimensional reactor (a reaction–diffusion cell). The boundaries of the reactor are permeable, so diffusion occurs from external reservoirs which contain fixed concentrations of the reactant and catalyst. The Galerkin method is used to approximate… (More)

- T. R. Marchant, Noel F Smyth
- Physical review. E, Statistical, nonlinear, and…
- 2006

Modulation theory is developed for a periodic peakon solution of the Camassa-Holm equation. An explicit simple wave solution of these modulation equations is then derived; this simple wave describing the evolution into an undular bore of an initial step. The characteristic on which the expansion fan occurs (propagating at a nonlinear group velocity) has a… (More)

- Gaetano Assanto, T. R. Marchant, A. A. Minzoni, Noel F Smyth
- Physical review. E, Statistical, nonlinear, and…
- 2011

We develop a modulation theory model based on a Lagrangian formulation to investigate the evolution of dark and gray optical spatial solitary waves for both the defocusing nonlinear Schrödinger (NLS) equation and the nematicon equations describing nonlinear beams, nematicons, in self-defocusing nematic liquid crystals. Since it has an exact soliton… (More)

- T. R. Marchant
- 2005

Exact and approximate solutions of the initial-boundary value problem for the Korteweg-de Vries equation on the semi-infinite line are found. These solutions are found for both constant and time-dependent boundary values. The form of the solution is found to depend markedly on the specific boundary and initial value. In particular, multiple solutions and… (More)

- K S Al Noufaey, T. R. Marchant, Maureen P. Edwards
- Mathematical biosciences
- 2015

Semi-analytical solutions for the diffusive Lotka-Volterra predator-prey system with delay are considered in one and two-dimensional domains. The Galerkin method is applied, which approximates the spatial structure of both the predator and prey populations. This approach is used to obtain a lower-order, ordinary differential delay equation model for the… (More)