相关论文: Mach reflection and KP solitons in shallow water

Shocks are ubiquitous in astrophysical sources, many of which involve relativistic bulk motions, leading to the formation of relativistic shocks. Such relativistic shocks have so far been studied mainly in one dimension, for simplicity, but…

In this paper we study the transformation of surface envelope solitons travelling over a bottom step in water of a finite depth. Using the transformation coefficients earlier derived in the linear approximation, we find the parameters of…

We prove large time asymptotics for solutions of the KP I equation with small initial data. Our assumptions on the initial data rule out lump solutions but give a precise description of the radiation field at large times. Our analysis uses…

In Part II of this series of papers, we consider an initial-boundary value problem for the Kolmogorov--Petrovskii--Piscounov (KPP) type equation with a discontinuous cut-off in the reaction function at concentration $u=u_c$. For fixed…

There is considerable fundamental and applicative interest in obtaining non-diffractive and non-dispersive spatio-temporal localized wave packets propagating in optical cubic nonlinear or Kerr media. Here, we analytically predict the…

The interaction of an oblique line soliton with a one-dimensional dynamic mean flow is analyzed using the Kadomtsev-Petviashvili II (KPII) equation. Building upon previous studies that examined the transmission or trapping of a soliton by a…

Two accelerated imaginary-time evolution methods are proposed for the computation of solitary waves in arbitrary spatial dimensions. For the first method (with traditional power normalization), the convergence conditions as well as…

We study weakly stable semilinear hyperbolic boundary value problems with highly oscillatory data. Here weak stability means that exponentially growing modes are absent, but the so-called uniform Lopatinskii condition fails at some boundary…

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…

The theory of the thin vapor layers linear optical properties is presented for the case of specular reflection of atoms colliding with the walls. The effects of light absorption and the shift in the resonance frequency are taken into…

The propagation and transformation of water waves over varying bathymetries is a subject of fundamental interest to ocean, coastal and harbor engineers. The specific bathymetry considered in this paper consists of one or two, naturally…

An experimental study is reported of the near-critical reflection of internal gravity waves over sloping topography in a stratified fluid. An overturning instability close to the slope and triggering the boundary-mixing process is observed…

We consider an effective scaling approach for the free expansion of a one-dimensional quantum wave packet, consisting in a self-similar evolution to be satisfied on average, i.e. by integrating over the coordinates. A direct comparison with…

An ultracold atom above a horizontal mirror experiences quantum reflection from the attractive Casimir-Polder interaction, which holds it against gravity and leads to quantum levitation states. We analyze this system by using a Liouville…

We study a class of 1+1 quadratically nonlinear water wave equations that combines the linear dispersion of the Korteweg-deVries (KdV) equation with the nonlinear/nonlocal dispersion of the Camassa-Holm (CH) equation, yet still preserves…

We study a long wave-length asymptotics for the Gross-Pitaevskii equation corresponding to perturbation of a constant state of modulus one. We exhibit lower bounds on the first occurence of possible zeros (vortices) and compare the…

An overview of the inverse scattering theory of the Kadomtsev Petviashvili II equation with an emphasis on the inverse problem for perturbed KP multi line solitons is provided. It is shown that, despite additional algebraic or analytic…

During the past decades the study of strongly interacting fluids experienced a tremendous progress. In the relativistic heavy ion accelerators, specially the RHIC and LHC colliders, it became possible to study not only fluids made of…

In this paper, the linear spectral problem, which associated with the (n+1)-dimensional generalized Kadomtsev-Petviashvili (gKP) equation, with the Jacobi elliptic function as the external potential is investigated based on the Lam\'{e}…

We consider a fifth-order Kadomtsev-Petviashvili equation which arises as a two-dimensional model in the classical water-wave problem. This equation possesses a family of generalized line solitary waves which decay exponentially to periodic…