相关论文: One-Two Dimensional Nonlinear Pulse Interaction

The emergence of confined structures and pattern formation are exceptional manifestations of concurring nonlinear interactions found in a variety of physical, chemical and biological systems[1]. Optical solitons are a hallmark of extreme…

In the first part of this series, an augmented PDE system was introduced in order to couple two nonlinear hyperbolic equations together. This formulation allowed the authors, based on Dafermos's self-similar viscosity method, to establish…

We study the dynamics of two-dimensional nonlinear ion-ion hybrid waves propagating perpendicular to an external magnetic field in plasmas with two ion species. We derive nonlinear equations for the envelope of electrostatic potential at…

We investigate theoretically the interaction of dark solitons in materials with a spatially nonlocal nonlinearity. In particular we do this analytically and for arbitrary degree of nonlocality. We employ the variational technique to show…

Inspired by the well known sine-Gordon equation, we present a symmetric coupled system of two real scalar fields in $1+1$ dimensions. There are three different topological soliton solutions which be labelled according to their topological…

A novel phenomenon is discovered that the short-range interaction between strongly nonlocal spatial solitons depends sinusoidally on their phase difference. The two neighbouring solitons at close proximate can be inter-trapped via the…

An ideal contrast-enhanced ultrasound image should display microbubble-induced nonlinearities while avoiding wave propagation nonlinearities. One of the most successful ultrasound pulse sequences to disentangle these nonlinear effects…

Nonlinear optical phenomena are typically local. Here we predict the possibility of highly nonlocal optical nonlinearities for light propagating in atomic media trapped near a nano-waveguide, where long-range interactions between the atoms…

We consider a planar two-dimensional system between two media with different dielectric constants and in the presence of a third dielectric medium separated by a nonplanar interface. Extending a perturbative method for solving Poisson's…

We study interactions between bright matter-wave solitons which acquire chiral transport dynamics due to an optically-induced density-dependent gauge potential. Through numerical simulations, we find that the collision dynamics feature…

We consider the modulational instability of nonlinearly interacting two-dimensional waves in deep water, which are described by a pair of two-dimensional coupled nonlinear Schroedinger equations. We derive a nonlinear dispersion relation.…

Some aspects of the connection between differential geometry and multidimensional soliton equations are discussed.

We present the discovery of a class of exact spatially localized as well as periodic wave solutions within the framework of the modified Korteweg-de Vries equation. This class comprises breather and interacting soliton solutions as well as…

In this work, we introduce a dispersive N(=2n)-wave interaction problem involving n velocities in two spatial dimensions and one temporal dimension. Exact solutions of the problem are exhibited. This is a generalization of the N-wave…

The interaction between two parallel beams in one-dimensional discrete saturable systems has been investigated using lithium niobate nonlinear waveguide arrays. When the beams are separated by one channel and in-phase it is possible to…

We study the stability, form and interaction of single and multiple dark solitons in quasi-one-dimensional dipolar Bose-Einstein condensates. The solitons are found numerically as stationary solutions in the moving frame of a non-local…

We consider KdV-type equations with $C^1$ nonhomogeneous nonlinearities and small dispersion $\varepsilon$. The first result consists in the conclusion that, in the leading term with respect to $\varepsilon$, the solitary waves in this…

Nonlinear dispersive partial differential equations such as the nonlinear Schr\"odinger equations can have solutions that blow-up. We numerically study the long time behavior and potential blowup of solutions to the focusing…

We develop a general theory of intertwined diffusion processes of any dimension. Our main result gives an SDE construction of intertwinings of diffusion processes and shows that they correspond to nonnegative solutions of hyperbolic partial…

We discuss existence and stability of two-dimensional solitons in media with spatially nonlocal nonlinear response. We show that such systems, which include thermal nonlinearity and dipolar Bose Einstein condensates, may support a variety…