Global ETD Search

1	Comparison of the Korteweg-de Vries (KdV) equation with the Euler equations with irrotational initial conditions Im, Jeong Sook 22 October 2010 (has links) No description available. Mathematics Shallow water waves KdV equation Euler equations Approximation Singularities
2	Wronskian and Gram Solutions to Integrable Equations using Bilinear Methods Wiggins, Benjamin 01 January 2017 (has links) This thesis presents Wronskian and Gram solutions to both the Korteweg-de Vries and Kadomtsev-Petviashvili equations, which are then scalable to arbitrarily large numbers of interacting solitons. Through variable transformation and use of the Hirota derivative, these nonlinear partial differential equations can be expressed in bilinear form. We present both Wronskian and Gram determinants which satisfy the equations. N=1,2,3 and higher order solutions are presented graphically; parameter tuning and the resultant behavioral differences are demonstrated and discussed. In addition, we compare these solutions to naturally occurring shallow water waves on beaches. bilinearization Hirota KdV KP shallow water waves Soliton Applied Mathematics Mathematics Physics