Related papers: Framework for the Forced Soliton Equation: Regular…
The Hirota transformation for the soliton solutions of the classical Sine-Gordon equation is suggestive of an extremely simple way for the construction of a nonlinear quantum-dynamical system of spin 1/2 particles that is equivalent to the…
Solitons are of the important significant in many fields of nonlinear science such as nonlinear optics, Bose-Einstein condensates, plamas physics, biology, fluid mechanics, and etc.. The stable solitons have been captured not only…
We derive the soliton matrices corresponding to an arbitrary number of higher-order normal zeros for the matrix Riemann-Hilbert problem of arbitrary matrix dimension, thus giving the complete solution to the problem of higher-order…
Half-space problems in the kinetic theory of gases are of great importance in the study of the asymptotic behavior of solutions of boundary value problems for the Boltzmann equation for small Knudsen numbers. In this work a generally…
We introduce soliton percolation phenomena in the nonlinear transport of light packets in suitable optical lattices with random properties. Specifically, we address lattices with a gradient of the refractive index in the transverse plane,…
Nontopological fermionic solitons exist across a diverse range of particle physics models and have rich cosmological implications. This study establishes a general framework for calculating fermionic soliton profiles under arbitrary scalar…
We consider a class of $N=2$ supersymmetric non--unitary theories in two--dimensional Minkowski spacetime which admit classical solitonic solutions. We show how these models can be twisted into a topological sector whose energy--momentum…
An overview is given of basic models combining discreteness in their linear parts (i.e. the models are built as dynamical lattices) and nonlinearity acting at sites of the lattices or between the sites. The considered systems include the…
We revisit the phenomenon of instability of solitons in the two dimensional generalization of the Korteweg-de Vries equation, the generalized Zakharov-Kuznetsov (ZK) equation, $u_t + \partial_{x_1} (\Delta u + u^p) = 0, (x_1,x_2) \in…
Dynamics of solitons is considered in the framework of the extended nonlinear Schrodinger equation (NLSE), which is derived from a system of Zakharov's type for the interaction between high- and low-frequency (HF and LF) waves, in which the…
We present a numerical solution in the form of a three-dimensional (3D) vortex soliton in unmagnetized plasma in the model of the generalized Zakharov equations with saturating exponential nonlinearity. To find the solution with a high…
We investigate numerically and theoretically the conditions leading to soliton ejection stimulated through the scattering of bright solitons by modulated reflectionless potential wells. Such potential wells allow for the possibility of…
For a polygon in Euclidean space we consider a transformation T which is obtained by applying the midpoints polygon construction twice and using an index shift. For a closed polygon this is a curve shortening process. A polygon is called…
The profiles of narrow lattice solitons are calculated analytically using perturbation analysis. A stability analysis shows that solitons centered at a lattice (potential) maximum are unstable, as they drift toward the nearest lattice…
We study a soliton in an optical lattice holding bosonic atoms quantum mechanically using both an exact numerical solution and quantum Monte Carlo simulations. The computation of the state is combined with an explicit account of the…
We investigate the soliton structure of novel (2+1)-dimensional nonlinear partial differential evolution(NLPDE) equations which may govern the behavior of a barothropic relaxing medium beneath high-frequency perturbations. As a result, we…
We propose a new approach to the theory of normal forms for Hamiltonian systems near a non-resonant elliptic singular point. We consider the space of all Hamiltonian functions with such an equilibrium position at the origin and construct a…
We derive a class of discrete nonlinear Schr{\"o}dinger (DNLS) equations for general polynomial nonlinearity whose stationary solutions can be found from a reduced two-point algebraic problem. It is demonstrated that the derived class of…
We study the stepwise sine-Gordon equation, in which the system parameter is different for positive and negative values of the scalar field. By applying appropriate boundary conditions, we derive relations between the soliton velocities…
We consider a class of ordinary differential equations describing one-dimensional systems with a quasi-periodic forcing term and in the presence of large damping. We discuss the conditions to be assumed on the mechanical force and the…