Related papers: Camassa-Holm cuspons, solitons and their interacti…
Formalism based on complex-scaling method is developed for solving the few particle scattering problem by employing only trivial boundary conditions. Several applications are presented proving efficiency of the method in describing elastic…
Lorentz scalar and mass interactions are studied in more detail in the framework of a reduced Dirac equation for heavy quark-antiquark mesons. A microscopic model for these interactions is proposed and analyzed. The charmonium mass spectrum…
This paper is concerned with the existence and uniqueness of global weak solutions to a generalized Camassa-Holm equation on real line. By introducing some new variables, the equation is transformed into two different semi-linear systems.…
We present two semidiscretizations of the Camassa-Holm equation in periodic domains based on variational formulations and energy conservation. The first is a periodic version of an existing conservative multipeakon method on the real line,…
To obtain new integrable nonlinear differential equations there are some well-known methods such as Lax equations with different Lax representations. There are also some other methods which are based on integrable scalar nonlinear partial…
We solve the problem of description for nonsingular pairs of compatible flat metrics in the general N-component case. The integrable nonlinear partial differential equations describing all nonsingular pairs of compatible flat metrics (or,…
We consider the 2D Maxwell--Lorentz system which describes a rotating particle coupled to the Maxwell field. The system admits stationary soliton-type solutions. We prove the attraction to solitons for any finite energy solution relying on…
Higher-order solitons, as well as simple $N$-soliton solutions, of the Gerdjikov-Ivanov equation are derived by the dressing method based on the technique of regularization. By the dressing transformation for the eigenfunction associated…
We investigate theoretically soliton excitations and dynamics of their formation in strongly correlated systems of ultracold bosonic atoms in two and three dimensional optical lattices. We derive equations of nonlinear hydrodynamics in the…
We establish the uniqueness of solutions of the Camassa-Holm equation on a finite interval with non-homogeneous boundary conditions in the case of bounded momentum. A similar result for the higher-order Camassa-Holm system is also given.…
The Boltzmann type kinetic equation for solitons in Nonlinear Schr\"{o}dinger equation has been constructed on the base of analysis of two soliton collision. Possible applications for Langmuir solitons in plasma and solitons in optic fiber…
A one-fold Darboux transformation between solutions of the semi-discrete massive Thirring model is derived using the Lax pair and dressing methods. This transformation is used to find the exact expressions for soliton solutions on zero and…
Kahan's method and a two-step generalization of the discrete gradient method are both linearly implicit methods that can preserve a modified energy for Hamiltonian systems with a cubic Hamiltonian. These methods are here investigated and…
Group theoretical methods are used to study the equations describing \chi^{(2)}:\chi^{(2)} cascading. The equations are shown not to be integrable by inverse scattering techniques. On the other hand, these equations do share some of the…
In this paper, we introduce and analyze a normalization method for solving a system of linear equations over tropical semirings. We use a normalization method to construct an associated normalized matrix, which gives a technique for solving…
Using the specific model of a system of like charged ions confined between two planar like charged surfaces, we compare the predictions for the energy and density profile of four simulation methods available to treat the long range Coulomb…
Dunajski generalization of the second heavenly equation is studied. A dressing scheme applicable to Dunajski equation is developed, an example of constructing solutions in terms of implicit functions is considered. Dunajski equation…
The duality between a class of the Davey-Stewartson type coupled systems and a class of two-dimensional Toda type lattices is discussed. A new coupled system related to the recently found lattice is presented. A method for eliminating…
In this letter, we construct new meshy soliton structures by using two concrete (2+1)-dimensional integrable systems. The explicit expressions based on corresponding Cole-Hopf type transformations are obtained. Constraint equation…
For a 2-component Camassa-Holm equation, as well as a 2-component generalization of the modified Camassa-Holm equation, nonlocal infinitesimal symmetries quadratically depending on eigenfunctions of linear spectral problems are constructed…