Numerical continuation of standing waves for the Davey-Stewartson equation
Sammanfattning: This thesis considers solitary standing wave solutions to the Davey-Stewart-son equation, which is a model for surface waves on a body of water in three dimensions. In a special case, the Davey-Stewartson equation is reduced to the well-known non-linear Schrödinger equation with cubic power which is known to have a countable familiy of radial standing waves. One of the aims of this thesis is to investigate whether this also is the case for the Davey-Stewartson equation by considering the linearization around these radial solutions. In particular, for the ground state it can be shown that the kernel is empty if we restrict the equation to even functions. We numerically investigate if the same is true for the excited states. Also, numerical continuation and bifurcation detection is done using the radial solutions as initial values.
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