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Jacob Brooks

Postgraduate Research Student
+44 (0)1483 683024
17 AA 04

Academic and research departments

Department of Mathematics.

My publications


Brooks Jacob, Derks Gianne, Lloyd David J.B. (2019) Existence of stationary fronts in a system of two coupled wave equations with spatial inhomogeneity,Nonlinearity32(11)pp. 4147-4187 London Mathematical Society
We investigate the existence of stationary fronts in a coupled system of two sine-Gordon equations with a smooth, ?hat-like? spatial inhomogeneity. The spatial inhomogeneity corresponds to a spatially dependent scaling of the sine-Gordon potential term. The uncoupled inhomogeneous sine-Gordon equation has stable stationary front solutions that persist in the coupled system. Carrying out a numerical investigation it is found that these inhomogeneous sine-Gordon fronts loose stability, provided the coupling between the two inhomogeneous sine-Gordon equations is strong enough, with new stable fronts bifurcating. In order to analytically study the bifurcating fronts, we first approximate the smooth spatial inhomogeneity by a piecewise constant function. With this approximation, we prove analytically the existence of a pitchfork bifurcation. To complete the argument, we prove that transverse fronts for a piecewise constant inhomogeneity persist for the smooth ?hat-like? spatial inhomogeneity by introducing a fast-slow structure and using geometric singular perturbation theory.