相关论文: Solution for (1+1) dimensional surface solitons in…
Solitary wave and soliton solutions of nonlinear equations are well known for physicists. A soliton is a solitary wave with some outstanding features which make it reasonable to be studied seriously in nonlinear systems. In fact most of the…
Using similarity transformations we construct explicit nontrivial solutions of nonlinear Schr\"odinger equations with potentials and nonlinearities depending on time and on the spatial coordinates. We present the general theory and use it…
An analytical linear solution of the fully compressible Euler equations is found, in the particular case of a stationary two dimensional flow that passes over an orographic feature with small height-width ratio. A method based on the…
We address the existence and properties of solitons in thermal media with periodic modulation of linear refractive index. Many kinds of solitons in such optical lattices, including symmetric and antisymmetric lattices, are found under…
Breather solutions are considered to be generally accepted models of rogue waves. However, breathers are not localized, while wavefields in nature can generally be considered as localized due to the limited spatial dimensions. Hence, the…
We introduce the simplest one-dimensional model of a dispersive optical medium with saturable dissipative nonlinearity and filtering (dispersive loss) which gives rise to stable solitary pulses (autosolitons). In the particular case when…
The existence of breather type solutions, i.e., periodic in time, exponentially localized in space solutions, is a very unusual feature for continuum, nonlinear wave type equations. Following an earlier work [Comm. Math. Phys. {\bf 302},…
We discover multipole-mode solitons supported by the surface between two distinct periodic lattices imprinted in Kerr-type nonlinear media. Such solitons are possible because the refractive index modulation at both sides of the interface…
We study the variational equations for solitons in noncommutative scalar field theories in an even number of spatial dimensions. We prove the existence of spherically symmetric solutions for a sufficiently large noncommutativity parameter…
We provide a review of non-topological solitonic solutions arising in theories with a complex scalar field and global or gauge $U(1)$-symmetry. It covers Q-balls, homogeneous charged scalar condensates, and nonlinear localized holes and…
We find non-BPS solutions of the noncommutative CP^1 model in 2+1 dimensions. These solutions correspond to soliton anti-soliton configurations. We show that the one-soliton one-anti-soliton solution is unstable when the distance between…
A brief review is given of some well-known and some very recent results obtained in studies of two- and three-dimensional (2D and 3D) solitons. Both zero-vorticity (fundamental) solitons and ones carrying vorticity S = 1 are considered.…
This article offers a review of results for solitons in 2D and 3D models of nonlinear dissipative media. The existence of such solitons requires to maintain two balances: between nonlinear self-focusing and linear diffraction and/or…
Interactions of noncommutative solitons in a modified U(n) sigma model in 2+1 dimensions can be analyzed exactly. Using an extension of the dressing method, we construct explicit time-dependent solutions of its noncommutative field equation…
Conditions of optimal (synchronized) collisions of any number of solitons and breathers are studied within the framework of the Gardner equation with positive cubic nonlinearity, which in the limits of small and large amplitudes tends to…
We discover the existence of vortex solitons supported by the surface between two optical lattices imprinted in Kerr-type nonlinear media. Such solitons can feature strongly noncanonical profiles, and we found that their properties are…
In this paper we study dynamics of solitons in the generalized nonlinear Schr\"odinger equation (NLS) with an external potential in all dimensions except for 2. For a certain class of nonlinearities such an equation has solutions which are…
In this paper, we give a proof of the existence of stationary dark soliton solutions or heteroclinic orbits of nonlinear equations of Schr\"odinger type with periodic inhomogeneous nonlinearity. The result is illustrated with examples of…
A non-Abelian gauge model with a complex isovector scalar field and a sixth-order self-interaction potential is considered. It is shown that it has a nontopological soliton solution. The features of this soliton include a monopole-like core…
We study partial analyticity of solutions to elliptic systems and analyticity of level sets of solutions to nonlinear elliptic systems. We consider several applications, including analyticity of flow lines for bounded stationary solutions…