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The Kadomtsev-Petviashvili (KP) equation describes weakly dispersive and small amplitude waves propagating in a quasi-two dimensional situation. Recently a large variety of exact soliton solutions of the KP equation has been found and…

Pattern Formation and Solitons · Physics 2015-03-14 Chiu-Yen Kao , Yuji Kodama

This article is a brief review of the results of studying the collapse of sound waves in media with positive dispersion, which is described in terms of the three-dimensional Kadomtsev-Petviashvili (KP) equation. The KP instability of…

Pattern Formation and Solitons · Physics 2022-09-07 E. A. Kuznetsov

The propagation of nonlinear and dispersive waves in various materials can be described by the well-known Kadomtsev-Petviashvili (KP) equation, which is a (2+1)-dimensional partial differential equation. In this paper, we show that the KP…

Mathematical Physics · Physics 2025-07-21 Harold Berjamin , Michel Destrade , Giuseppe Saccomandi

The KP-I equation arises as a weakly nonlinear model equation for gravity-capillary waves with Bond number $\beta>1/3$, also called strong surface tension. This equation has recently been shown to have a family of nondegenerate, symmetric…

Analysis of PDEs · Mathematics 2025-12-18 Mats Ehrnström , Mark D. Groves

We study the generalization of the dispersionless Kadomtsev - Petviashvili (dKP) equation in n+1 dimensions and with nonlinearity of degree m+1, a model equation describing the propagation of weakly nonlinear, quasi one dimensional waves in…

Exactly Solvable and Integrable Systems · Physics 2016-10-12 F. Santucci , P. M. Santini

Full dispersive models of water waves, such as the Whitham equation and the full dispersion Kadomtsev-Petviashvili (KP) equation, are interesting from both the physical and mathematical points of view. This paper studies analogous full…

Mathematical Physics · Physics 2022-08-15 H. A. Erbay , S. Erbay , A. Erkip

The celebrated (1+1)-dimensional Korteweg de-Vries (KdV) equation and its (2+1)-dimensional extention, the Kadomtsev-Petviashvili (KP) equation, are two of the most important models in physical science. The KP hierarchy is explicitly…

Exactly Solvable and Integrable Systems · Physics 2020-08-26 S. Y. Lou

The purpose of this paper is to expand the recent work of Sardar et al. [Phys. Plasmas 23, 123706 (2016)] on the existence and stability of alternative dust ion acoustic solitary wave solution of the combined modified Kadomtsev Petviashvili…

Plasma Physics · Physics 2018-10-16 Sankirtan Sardar , Anup Bandyopadhyay , K. P. Das

The Kadomtsev-Petviashvili (KP) equation possesses a four-parameter family of one-dimensional periodic traveling waves. We study the spectral stability of the waves with small amplitude with respect to two-dimensional perturbations which…

Analysis of PDEs · Mathematics 2010-05-02 Mariana Haragus

A complete classification of compacton solutions is carried out for a generalization of the Kadomtsev-Petviashvili (KP) equation involving nonlinear dispersion in two and higher spatial dimensions. In particular, precise conditions are…

Mathematical Physics · Physics 2025-10-20 Stephen C. Anco , Maria Gandarias

The KP-I equation \[ (u_t-2uu_x+\tfrac{1}{2}(\beta-\tfrac{1}{3})u_{xxx})_x -u_{yy}=0 \] arises as a weakly nonlinear model equation for gravity-capillary waves with strong surface tension (Bond number $\beta>1/3$). This equation admits ---…

Analysis of PDEs · Mathematics 2018-11-14 Mats Ehrnström , Mark Groves

In this paper, we delve into the study of the generalized KP equation, which incorporates double-power nonlinearities. Our investigation covers various aspects, including the existence of solitary waves, their nonlinear stability, and…

Analysis of PDEs · Mathematics 2023-12-05 Amin Esfahani , Steven Levandosky , Gulcin M. Muslu

The modified Kadomtsev-Petviashvili (mKP) equation is shown in this paper to be decomposable into the first two soliton equations of the 2N-coupled Chen-Lee-Liu and Kaup-Newell hierarchies by respectively nonlinearizing two sets of symmetry…

Mathematical Physics · Physics 2009-11-13 Tao Xu , Hai-Qiang Zhang , Ya-Xing Zhang , Juan Li , Bo Tian

By considering the inhomogeneities of media, a generalized variable-coefficient Kadomtsev-Petviashvili (vc-KP) equation is investigated, which can be used to describe many nonlinear phenomena in fluid dynamics and plasma physics. In this…

Exactly Solvable and Integrable Systems · Physics 2015-06-03 Shou-Fu Tian , Hong-Qing Zhang

In nonlinear physics, the interactions among solitons are well studied thanks to the multiple soliton solutions can be obtained by various effective methods. However, it is very difficult to study interactions among different types of…

Exactly Solvable and Integrable Systems · Physics 2012-08-17 Xue-Ping Cheng , Chun-Li Chen , Sen-Yue Lou

We study the (n+1)-dimensional generalization of the dispersionless Kadomtsev-Petviashvili (dKP) equation, a universal equation describing the propagation of weakly nonlinear, quasi one dimensional waves in n+1 dimensions, and arising in…

Exactly Solvable and Integrable Systems · Physics 2015-05-14 S. V. Manakov , P. M. Santini

We consider the initial value problems of the Kadomtsev-Petviashvili (KP) equation for symmetric V-shape initial waves consisting of two semi-infinite line solitons with the same amplitude. Numerical simulations show that the solutions of…

Exactly Solvable and Integrable Systems · Physics 2015-05-13 Yuji Kodama , Masayuki Oikawa , Hidekazu Tsuji

Sardar et al. [Phys. Plasmas 23, 073703 (2016)] have studied the stability of small amplitude dust ion acoustic solitary waves in a collisionless unmagnetized electron - positron - ion - dust plasma. They have derived a Kadomtsev…

Plasma Physics · Physics 2018-10-16 Sankirtan Sardar , Anup Bandyopadhyay , K. P. Das

In the paper we investigate integrability characteristics for the dispersionless Kadomtsev-Petviashvili hierarchy. These characteristics include symmetries, Hamiltonian structures and conserved quantities. We give a Lax triad to construct a…

Exactly Solvable and Integrable Systems · Physics 2014-07-28 Wei Fu , R. Ilangovane , K. M. Tamizhmani , Da-jun Zhang

Dynamics of the Fermi-Pasta-Ulam (FPU) system on a two-dimensional square lattice is considered in the limit of small-amplitude long-scale waves with slow transverse modulations. In the absence of transverse modulations, dynamics of such…

Analysis of PDEs · Mathematics 2022-09-28 Nikolay Hristov , Dmitry E. Pelinovsky
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