Related papers: Backlund transformations, Ward solitons, and unito…
In this work we offer an approach to enlarge the number of exactly solvable models with two real scalar fields in (1+1)D. We build some new two-field models, and obtain their exact orbits and exact or numerical field configurations. It is…
We study to unify soliton systems, KdV/mKdV/sinh-Gordon, through SO(2,1) $\cong$ GL(2,$\mathbb R$) $\cong$ M\"{o}bius group point of view, which might be a keystone to exactly solve some special non-linear differential equations. If we…
We introduce multi-soliton sets in the two-dimensional medium with the second-harmonic-generating nonlinearity subject to spatial modulation in the form of a triangle of singular peaks. Various families of symmetric and asymmetric sets are…
A linear system, which generates a Moyal-deformed two-dimensional soliton equation as integrability condition, can be extended to a three-dimensional linear system, treating the deformation parameter as an additional coordinate. The…
A four-dimensional topological field theory is introduced which generalises $B\wedge F$ theory to give a Bogomol'nyi structure. A class of non-singular, finite-Action, stable solutions to the variational field equations is identified. The…
We propose a discrete Darboux-Lax scheme for deriving auto-B\"acklund transformations and constructing solutions to quad-graph equations that do not necessarily possess the 3D consistency property. As an illustrative example we use the…
The modified Bernoulli numbers $B_{n}^{*}$ considered by Zagier are generalized to modified N\"orlund polynomials ${B_{n}^{(\ell)*}}$. For $\ell\in\mathbb{N}$, an explicit expression for the generating function for these polynomials is…
Symmetry of SDYM equations for "physically restricted solution" with hermitian group element $G=G^H$ in representation of Yang is described. Such transformation $D^B$ pass some PRS to the new one of the same kind. Transformation contain…
A one parameter generalization of Ward's chiral model in 2+1 dimensions is given. Like the original model the present one is integrable and possesses a positive-definite and conserved energy and $y$-momentum. The details of the scattering…
Binary constrained flows of soliton equations admitting $2\times 2$ Lax matrices have 2N degrees of freedom, which is twice as many as degrees of freedom in the case of mono-constrained flows. For their separation of variables only N pairs…
We develop a wide general theory of bilinear bi-parameter singular integrals $T$. First, we prove a dyadic representation theorem starting from $T1$ assumptions and apply it to show many estimates, including $L^p \times L^q \to L^r$…
We consider an hierarchy of integrable 1+2-dimensional equations related to Lie algebra of the vector fields on the line. The solutions in quadratures are constructed depending on $n$ arbitrary functions of one argument. The most…
We study soliton solutions to the Klein-Gordon equation via Lie symmetries and the travelling-wave ansatz. It is shown, by taking a linear combination of the spatial and temporal Lie point symmetries, that soliton solutions naturally exist,…
A bilinear formulation for the supersymmetric two-boson equation is derived. As applications, some solutions are calculated for it. We also construct a bilinear Backlund transformation.
We construct the supersymmetric extensions of the Darboux-Backlund transformations (DBTs) for the Manin-Radul super KdV hierarchy using the super-pseudo-differential operators. The elementary DBTs are triggered by the gauge operators…
We investigate a version of the abelian Higgs model with a non-standard kinetic term (K field theory) in 2+1 dimensions. The existence of vortex type solutions with compact support (topological compactons) is established by a combination of…
In earlier works on Shape Dynamics (SD), a linear method of solving a particular set of Lichnerowicz-type equations through the implicit function theorem was developed in order to implicitly construct SD's global Hamiltonian and eliminate…
Very narrow spatial bright solitons in (1+1)D and (2+1)D versions of cubic-quintic and full saturable models are studied, starting from the full system of the Maxwell's equations, rather than from the paraxial (NLS) approximation. For the…
This work establishes a multivariable Wold-type decomposition for left-inverse commuting $n$-tuples of bounded operators, built on the hypothesis that each component admits a Wold-type decomposition. For pairs of operators, we obtain a…
We construct the first analytic examples of topologically non-trivial solutions of the (3+1)-dimensional $U(1)$ gauged Skyrme model within a finite box in (3+1)-dimensional flat space-time. There are two types of gauged solitons. The first…