Related papers: Characteristic analysis for integrable soliton mod…
We study nonlocal bright solitons subject to external spatially nonuniform potentials. If the potential is slowly varying on the soliton scale, we derive analytical soliton solutions behaving like Newtonian particles. If the potential has…
In self-tuning brane-world models with extra dimensions, large contributions to the cosmological constant are absorbed into the curvature of extra dimensions and consistent with flat 4d geometry. In models with conventional Lagrangians…
Stability is a key property of both forward models and inverse problems, and depends on the norms considered in the relevant function spaces. For instance, stability estimates for hyperbolic partial differential equations are often based on…
Novel soliton structures are constructed for the Fokas-Lenells equation. In so doing, and after discussing the stability of continuous waves, a multiple scales perturbation theory is used to reduce the equation to a Korteweg-de Vries system…
Embedded solitons are exceptional modes in nonlinear-wave systems with the propagation constant falling in the system's propagation band. An especially challenging topic is seeking for such modes in nonlinear dynamical lattices (discrete…
In this work, we present a detailed study of the dynamics and stability of fundamental spatiotemporal solitons emerging in multimode waveguides with a parabolic transverse profile of the linear refractive index. Pulsed beam propagation in…
The article studies Lorentz-invariant 2D equations with long-lived ($t \backsim 1000$ ) localized solutions. In the case of three scalar fields localized solutions with a nontrivial internal structure similar to the hadron structure are…
We develop a general theory of spatial solitons in a liquid crystalline medium exhibiting a nonlinearity with an arbitrary degree of effective nonlocality. The model accounts the observability of "accessible solitons" and establishes an…
We discover a new class of topological solitons. These solitons can exist in a space of infinite volume like, e.g., $\mathbb{R}^n$, but they cannot be placed in any finite volume, because the resulting formal solutions have infinite energy.…
In this article, we consider mechanical billiard systems defined with Lagrange's integrable extension of Euler's two-center problems in the Euclidean space, on the sphere, and in the hyperbolic space of arbitrary dimension $n \ge 3$. In the…
We formulate the necessary conditions for the integrability of a certain family of Hamiltonian systems defined in the constant curvature two-dimensional spaces. Proposed form of potential can be considered as a counterpart of a homogeneous…
We consider deformations of the $SU(3)$ Affine Toda theory (AT) and investigate the integrability properties of the deformed theories. We find that for some special deformations all conserved quantities change to being conserved only…
A Lagrangian based method is used to derive an analytical model for studying the dynamics of matter-wave bright soliton created in a harmonic potential which is attractive in the transverse direction and expulsive in the longitudinal…
We present the first method to directly use a learned continuous Lagrangian to forecast the dynamics of systems governed by partial differential equations, exploiting the inherent conservative structure to achieve stable long-range…
A heavy top with a fixed point and a rigid body in an ideal fluid are important examples of Hamiltonian systems on a dual to the semidirect product Lie algebra $e(n)=so(n)\ltimes\mathbb R^n$. We give a Lagrangian derivation of the…
This paper studies the existence of invariant smooth Lagrangian graphs for Tonelli Hamiltonian systems with symmetries. In particular, we consider Tonelli Hamiltonians with n independent but not necessarily involutive constants of motion…
A family of systems related to a linear and bilinear evolution of roots of polynomials in the complex plane is considered. Restricted to the line, the evolution induces dynamics of the Coulomb charges in external potentials, while its fixed…
We have found various families of two-dimensional spatiotemporal solitons in quadratically nonlinear waveguide arrays. The families of unstaggered odd, even and twisted stationary solutions are thoroughly characterized and their stability…
By a semi-Lagrangian change of coordinates, the hydrostatic Euler equations describing free-surface sheared flows is rewritten as a system of quasilinear equations, where stability conditions can be determined by the analysis of its…
The study of noncommutative solitons is greatly facilitated if the field equations are integrable, i.e. result from a linear system. For the example of a modified but integrable U(n) sigma model in 2+1 dimensions we employ the dressing…