title: On the integrable elliptic cylindrical Kadomtsev-Petviashvili equation.
abstract: There exist two versions of the Kadomtsev-Petviashvili (KP) equation, related to the Cartesian and cylindrical geometries of the waves. In this paper, we derive and study a new version, related to the elliptic cylindrical geometry. The derivation is given in the context of surface waves, but the derived equation is a universal integrable model applicable to generic weakly nonlinear weakly dispersive waves. We also show that there exist nontrivial transformations between all three versions of the KP equation associated with the physical problem formulation, and use them to obtain new classes of approximate solutions for water waves.
authors.affiliation: Department of Mathematical Sciences, Loughborough University, Loughborough LE11 3TU, United Kingdom. K.Khusnutdinova@lboro.ac.uk
authors.forename: K R
authors.initials: KR
authors.lastname: Khusnutdinova
authors.forename: C
authors.initials: C
authors.lastname: Klein
authors.forename: V B
authors.initials: VB
authors.lastname: Matveev
authors.forename: A O
authors.initials: AO
authors.lastname: Smirnov
mesh_terms: D001274:Atmospheric Pressure; D006112:Gravitation; D009038:Motion; D017711:Nonlinear Dynamics; D013500:Surface Tension; D013997:Time Factors; D014867:Water; D014872:Water Movements
chemical_list: D014867:Water