Loading…

QR Code

On the integrable elliptic cylindrical Kadomtsev-Petviashvili equation

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 der...

Full description

Saved in:

Bibliographic Details
Main Authors:	Karima Khusnutdinova, C. Klein, Vladimir S. Matveev, A.O. Smirnov
Format:	Default Article
Published:	2013
Subjects:	Other mathematical sciences not elsewhere classified untagged Mathematical Sciences not elsewhere classified
Online Access:	https://hdl.handle.net/2134/15723
Tags:	Add Tag No Tags, Be the first to tag this record!

Similar Items

Interaction of two lump solitons described by the Kadomtsev-Petviashvili I equation
by: Zhiming Lu, et al.
Published: (2003)

Flux singularities in multiphase wavetrains and the Kadomtsev-Petviashvili equation with applications to stratified hydrodynamics
by: Daniel Ratliff
Published: (2018)

Lame equation, quantum top and elliptic Bernoulli polynomials.
by: Marie-Pierre J.E. Grosset, et al.
Published: (2005)

Nonlinear waves in a bi-layer and coupled Klein-Gordon equations
by: Karima Khusnutdinova
Published: (2002)

Coupled Klein-Gordon equations and energy exchange in two-component systems
by: Karima Khusnutdinova
Published: (2007)

Computational techniques for the numerical solution of parabolic and elliptic partial differential equations
by: Christopher R. Gane
Published: (1974)

Integrable equations of the dispersionless Hirota type and hypersurfaces in the Lagrangian Grassmannian
by: Evgeny Ferapontov, et al.
Published: (2007)

On radiating solitary waves in bi-layers with delamination and coupled Ostrovsky equations
by: Karima Khusnutdinova, et al.
Published: (2017)

Nonlinear waves in integrable and nonintegrable systems' by Jianke Yang (SIAM, Philadelphia, 2010) [book review].
by: Karima Khusnutdinova
Published: (2015)

Extremal rational elliptic threefolds
by: Artie Prendergast
Published: (2010)

Elliptic fibrations on cubic surfaces
by: Gavin Brown, et al.
Published: (2010)

A new integrable system on the sphere
by: Holger R. Dullin, et al.
Published: (2004)

Validity of the weakly nonlinear solution of the cauchy problem for the boussinesq-type equation
by: Karima Khusnutdinova, et al.
Published: (2014)

Resonant elliptic equilibria in Hamiltonian systems
by: Sven Schmidt
Published: (2008)

Rotational acoustic resonances in cylindrical waveguides
by: Yuting Duan, et al.
Published: (2003)

Soliton solutions to the fifth-order Korteweg–de Vries equation and their applications to surface and internal water waves
by: Karima Khusnutdinova, et al.
Published: (2018)

Hydrodynamic reductions of multidimensional dispersionless PDEs: The test for integrability
by: Evgeny Ferapontov, et al.
Published: (2003)

A new method to construct integrable equations.
by: C. Hoenselaers
Published: (2005)

Radiating solitary waves in coupled Boussinesq equations
by: Roger Grimshaw, et al.
Published: (2017)

The cone conjecture for some rational elliptic threefolds
by: Artie Prendergast
Published: (2012)

Trapping of waves by a submerged elliptical torus
by: Maureen McIver, et al.
Published: (2001)

Elliptic Faulhaber polynomials and Lame densities of states
by: Marie-Pierre J.E. Grosset, et al.
Published: (2005)

Trapped modes in cylindrical waveguides
by: Christopher Linton, et al.
Published: (1998)

D'Alembert-type solution of the Cauchy problem for the Boussinesq-Klein-Gordon equation
by: Karima Khusnutdinova, et al.
Published: (2019)

Periodic solutions of coupled Boussinesq equations and Ostrovsky-type models free from zero-mass contradiction
by: Karima Khusnutdinova, et al.
Published: (2022)

Integrable equations of the dispersionless Hirota type
by: Lenos Hadjikos
Published: (2009)

Integrability of nonabelian differential-difference equations: The symmetry approach
by: Vladimir Novikov, et al.
Published: (2024)

Forward-backward stochastic differential equations on infinite horizon and quasilinear elliptic PDEs
by: Yufeng Shi, et al.
Published: (2019)

Coupled Ostrovsky equations for internal waves in a shear flow
by: A. Alias, et al.
Published: (2014)

The numerical solution of singular non-linear integral equations
by: Raymond C. Forbes
Published: (1984)

Weakly-nonlinear solution of coupled Boussinesq equations and radiating solitary waves
by: Karima Khusnutdinova, et al.
Published: (2019)

Development of numerical methods for the solution of integral equations
by: Anthony P.G. Morgan
Published: (1984)

Water-wave propagation through an infinite array of cylindrical structures
by: Philip McIver
Published: (1999)

On a class of 2D integrable lattice equations
by: Evgeny Ferapontov, et al.
Published: (2020)

Cauchy problem for integrable discrete equations on quad-graphs
by: V.E. Adler, et al.
Published: (2003)

Supplementary information files for: Periodic solutions of coupled Boussinesq equations and Ostrovsky-type models free from zero-mass contradiction
by: Karima Khusnutdinova, et al.
Published: (2022)

Calabi-Yau threefolds fibred by Kummer surfaces associated to products of elliptic curves
by: Charles F. Doran, et al.
Published: (2016)

On integrability of (2+1)-dimensional quasilinear systems.
by: Evgeny Ferapontov, et al.
Published: (2003)

An integral equation approach to continuous system identification and model reduction
by: Nouari Messali
Published: (1988)

The characterization of two-component (2+1)-dimensional integrable systems of hydrodynamic type
by: Evgeny Ferapontov, et al.
Published: (2003)