Similarity Solutions of Some Two‐Space‐Dimensional Nonlinear Wave Evolution Equations

摘要

Similarity reductions of the two‐space‐dimensional versions of the Korteweg‐deVries, modified Korteweg‐deVries, Benjamin‐Davis‐Ono, and nonlinear Schrödinger equations are presented, and some solutions of the reduced equations are discussed. Exact dispersive solutions of the two‐dimensional Korteweg‐deVries equation are obtained, and the similarity solution of this equation is shown to be reducible to the second Painl