The Journal of The Australian Mathematical Society. Series B. Applied Mathematics 

About: The Journal of The Australian Mathematical Society. Series B. Applied Mathematics is an academic journal. The journal publishes majorly in the area(s): Differential equation & Nonlinear system. Over the lifetime, 791 publications have been published receiving 12379 citations.

Water waves, nonlinear Schrödinger equations and their solutions

Abstract: Equations governing modulations of weakly nonlinear water waves are described. The modulations are coupled with wave-induced mean flows except in the case of water deeper than the modulation length scale. Equations suitable for water depths of the order the modulation length scale are deduced from those derived by Davey and Stewartson [5] and Dysthe [6]. A number of ases in which these equations reduce to a one dimensional nonlinear Schrodinger (NLS) equation are enumerated.Several analytical solutions of NLS equations are presented, with discussion of some of their implications for describing the propagation of water waves. Some of the solutions have not been presented in detail, or in convenient form before. One is new, a “rational” solution describing an “amplitude peak” which is isolated in space-time. Ma's [13] soli ton is particularly relevant to the recurrence of uniform wave trains in the experiment of Lake et al.[10].In further discussion it is pointed out that although water waves are unstable to three-dimensional disturbances, an effective description of weakly nonlinear two-dimensional waves would be a useful step towards describing ocean wave propagation.

What is invexity

Abstract: Recently it was shown that many results in Mathematical Programming involving convex functions actually hold for a wider class of functions, called invex. Here a simple characterization of invexity is given for both constrained and unconstrained problems. The relationship between invexity and other generalizations of convexity is illustrated. Finally, it is shown that invexity can be substituted for convexity in the saddle point problem and in the Slater constraint qualification.

The numerical solution of stochastic differential equations

Abstract: A method is proposed for the numerical solution of Ito stochastic differential equations by means of a second-order Runge–Kutta iterative scheme rather than the less efficient Euler iterative scheme. It requires the Runge–Kutta iterative scheme to be applied to a different stochastic differential equation obtained by subtraction of a correction term from the given one.

On generalised convex mathematical programming

Abstract: The sufficient optimality an conditiond duality results s have recently been givenfor the following generalised convex programming problem:Minimise f(x) subjec, t t o g(x) 0,for some r\: X o x X o —> R" .It is shown here that a relaxation definin thge above generalised convexity leadsto a new class of multi-objective problems which preserve thse sufficient optimalityand duality results in the scalar case, and avoids the major difficulty of verifying thatthe inequality hold fosr the same functio rj(.,n Further .). , this relaxation allowsone to treat certain nonlinear multi-objective fractional programming problems andsome other classe osf nonlinear (composite) problem as specias l cases. 1. Introduction Consider the constrained multi-objective optimisation problem(VP) V-Minimis (/, (*),... , f p (x)) subjec to g(x)e R and g: Xo —> R

Modelling the spread of grass fires

Abstract: A simple elliptic model is developed for the spread of a fire front through grassland. This is used to predict theoretical fire fronts, which agree closely with those obtained in practice.