A solitary wave application of an iterative method for nonlinear elliptic eigenvalue problems

AbstractA basic problem is that of solving nonlinear elliptic eigenvalue problems in the plane. Problems of this type arise in many branches of physics and engineering. The particular problem considered here, internal solitary waves in stratified fluids, occurs in fluid dynamics. An iterative technique (based on a transformation of the objective functional in an equivalent variational formulation of the problem) is used to numerically solve for eigenvalues and eigenfunctions associated with the fluid system. The choice of implementation involves discretizing the problem using finite Fourier sine series in conjunction with fast Fourier transforms (FFT). Results from preliminary test problems indicate that this numerical method can be used to verify the range of validity of existing (analytic) asymptotic expansion methods, and that new large amplitude solutions (strongly nonlinear waves) that cannot be obtained from the existing asymptotic expansion methods can be obtained using this numerical method