Related papers: Mach reflection and KP solitons in shallow water
The main purpose of the paper is to provide a survey of our recent studies on soliton solutions of the Kadomtsev-Petviashvili (KP) equation. The classification is based on the far-field patterns of the solutions which consist of a finite…
This gives a survey of our recent studies on soliton solutions of the Kadomtsev-Petviashvili equation with an emphasis on the Mach reflection problem in shallow water.
The oblique collisions and dynamical interference patterns of two-dimensional dispersive shock waves are studied numerically and analytically via the temporal dynamics induced by wedge-shaped initial conditions for the…
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…
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…
The dynamics of initially truncated and bent line solitons for the Kadomtsev-Petviashvili (KPII) equation modelling internal and surface gravity waves are analysed using modulation theory. In contrast to previous studies on obliquely…
In this work, we study solitary waves in a (2+1)-dimensional variant of the defocusing nonlinear Schr\"odinger (NLS) equation, the so-called Camassa-Holm NLS (CH-NLS) equation. We use asymptotic multiscale expansion methods to reduce this…
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…
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 ---…
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…
Resonant Y-shaped soliton solutions to the Kadomtsev-Petviashvili II (KPII) equation are modelled as shock solutions to an infinite family of modulation conservation laws. The fully two-dimensional soliton modulation equations, valid in the…
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…
The conformal mapping approach is a well established technique for solving the Euler equations for potential flows with one spatial dimension. In this work, we extend this framework to problems with a weakly transversal dependence and, by…
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…
A detailed numerical study of the long time behaviour of dispersive shock waves in solutions to the Kadomtsev-Petviashvili (KP) I equation is presented. It is shown that modulated lump solutions emerge from the dispersive shock waves. For…
There exist two versions of the Kadomtsev-Petviashvili 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…
The Camassa-Holm-Kadomtsev-Petviashvili-I equation (CH-KP-I) is a two dimensional generalization of the Camassa-Holm equation (CH). In this paper, we prove transverse instability of the line solitary waves under periodic transverse…
In recent papers, denoted by MG24, MG25 in this text, we used the Korteweg-de Vries (KdV) equation and its two-dimensional extension, the Kadomtsev-Petviashvili (KP) equation to describe the evolution of wind-driven water wave packets in…
Internal waves propagate obliquely through a stratified fluid with an angle that is fixed with respect to gravity. Upon reflection on a sloping bed, striking phenomena are expected to occur close to the slope. We present here laboratory…
The investigation of dynamics of intense solitary wave groups of collinear surface waves is performed by means of numerical simulations of the Euler equations and laboratory experiments. The processes of solitary wave generation, reflection…