A potential representation for the subset of traveling solutions of nonlinear dispersive evolution equations is introduced. The procedure involves a reduction of a third order partial differential equation to a first order ordinary differential equation. In this representation it can be shown that solitons and solutions with compact support only exist in systems with linear or quadratic dispersion, respectively. In particular, this article deals with so the called K(n,m) equations. It is shown that these equations can be classified according to a simple point transformation. As a result, all equations that allow for soliton solutions join the same equivalence class with the Korteweg-deVries equation being its representative.
Solitons of nonlinear dispersive wave steered from Navier-Bernoulli hypothesis and Love's hypothesis in the cylindrical elastic rod with compressible Murnaghan's materials
Space-time resonances in the spatiotemporal spectrum of nonlinear dispersive waves
Courant Institute of Mathematical Sciences, New York University（纽约大学库朗数学科学研究所）；Department of Mathematics, University of Toronto（多伦多大学数学系）；Department of Naval Architecture and Marine Engineering, University of Michigan（密歇根大学船舶与海洋工程系）
