73 citations · 343 across the 31 of their papers we have counts for
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math.AP2014
Petviashvilli's Method for the Dirichlet Problem
Derek Olson, Soumitra Shukla, Gideon Simpson +1
We examine the Petviashvilli method for solving the equation on a bounded domain with Dirichlet boundary conditions. We prove a local…
math.AP2014★ 61 cited
Asymptotic Stability of high-dimensional Zakharov-Kuznetsov solitons
Raphaël Côte, Claudio Muñoz, Didier Pilod +1
We prove that solitons (or solitary waves) of the Zakharov-Kuznetsov (ZK) equation, a physically relevant high dimensional generalization of the Korteweg-de Vries (KdV) equation ap…
math.AP2014
Local Existence Theory for Derivative Nonlinear Schrödinger Equations with Non-Integer Power Nonlinearities
David M. Ambrose, Gideon Simpson
We study a derivative nonlinear Schrödinger equation, allowing non-integer powers in the nonlinearity, . Making careful use of the energy method, we are able to estab…