While the half-angle which encloses a Kelvin ship wave pattern is commonly accepted to be
19.47°, recent observations and calculations for sufficiently fast-moving ships suggest that …

We develop a time-dependent conformal method to study the effect of viscosity on steep
surface waves. When the effect of surface tension is included, numerical solutions are found …

Burgers' equation is an important mathematical model used to study gas dynamics and
traffic flow, among many other applications. Previous analysis of solutions to Burgers' …

The inverse problem of steady two-dimensional open channel free-surface flow is
considered, with the focus on determining two types of disturbances: a surface pressure …

The surface gravity wave pattern that forms behind a steadily moving disturbance is well
known to comprise divergent waves and transverse waves, contained within a distinctive …

We study homoclinic snaking in the cubic-quintic Swift–Hohenberg equation (SHE) close to
the onset of a subcritical pattern-forming instability. Application of the usual multiple-scales …

An efficient numerical method to compute nonlinear solutions for 2D steady free-surface flow
over an arbitrary channel bottom topography is presented. The approach is based on a …

The nonlinear problem of steady free-surface flow past a submerged source is considered
as a case study for three-dimensional ship wave problems. Of particular interest is the …

We investigate geometric aspects of co-equational parametric resurgence, by studying
physical problems whose formal asymptotic solutions give rise to Borel transforms lying on …

We study asymptotic solutions to a singularly perturbed, period-2 Toda lattice and use
exponential asymptotics to examine “nanoptera,” which are nonlocal solitary waves with …