Related papers: Soliton dynamics to the coupled Higgs equation and…
We study the integrable systems in higher dimensions which can be written not by the Hirota's bilinear form but by the trilinear form. We explicitly discuss about the Bogoyavlenskii-Schiff(BS) equation in (2 + 1) dimensions. Its analytical…
We construct various types of degenerate multi-soliton and multi-breather solutions for the sine-Gordon equation based on B\"{a}cklund transformations, Darboux-Crum transformations and Hirota's direct method. We compare the different…
Explicit solutions to the related integrable nonlinear evolution equations are constructed by solving the inverse scattering problem in the reflectionless case for the third-order differential equation $d^3\psi/dx^3+Q\,d\psi/dx+P\psi…
A system of coupled scalar fields is introduced which possesses a spectrum of massive single-soliton solutions. Some of these solutions are unstable and decay into lower mass stable solitons. Some properties of the solutions are obtained…
Physically relevant soliton solutions of the resonant nonlinear Schrodinger (RNLS) equation with nontrivial boundary conditions, recently proposed for description of uniaxial waves in a cold collisionless plasma, are considered in the…
Recently, we have found an exact solution to the full set of Dyson-Schwinger equations of the non-interacting part of the Higgs sector of the Standard Model obtained by solving the 1-point correlation function equation. In this work we…
Self-dual vortex solutions are studied in detail in the generalized abelian Higgs model with independent Chern-Simons interaction. For special choices of couplings, it reduces to a Maxwell-Higgs model with two scalar fields, a…
In this study, we investigate the Klein-Gordon-Zakharov system with a focus on identifying multi-soliton solutions. Specifically, for a given number $N$ of solitons, we demonstrate the existence of a multi-soliton solution that…
Hirota's method is used to construct multi--soliton and plane--wave solutions for affine Toda field theories with imaginary coupling.
We study a simple nonlinear vector model defined on the honeycomb lattice. We propose a bilinearization scheme for the field equations and demonstrate that the resulting system is closely related to the well-studied integrable models, such…
A scalar singlet, coupled to the other particles only through its mixing with the Higgs boson, appears in several motivated extensions of the Standard Model. The prospects for the discovery of a generic singlet at the various stages of the…
In this paper we study the coupling of scalar (Higgs) particles ($\phi$) with gravitons ($h$) and their possible effects. The general form of the 3-point interaction $\phi(p) h(1)h(2)$ can be derived using the scaling behavior of the spinor…
The DP equation is investigated from the point of view of determinant-pfaffian identities. The reciprocal link between the Degasperis-Procesi (DP) equation and the pseudo 3-reduction of the $C_{\infty}$ two-dimensional Toda system is used…
Solitons and cavitons (localized solutions with singularities) for the nonlocal Whitham equations are studied. The equation of a fourth order with a parameter in front of fourth derivative for traveling waves is reduced to a reversible…
By introducing generalized Backlund Transformations depending on arbitrary functions, wave and localized soliton solutions of the Davey- Stewartson equations are generated. Moreover explicit soliton solutions of the Hamiltonian DSI and…
The multi-soliton solution of the sine-Gordon equation in the presence of elliptic-function background is derived by the inverse scattering method. The key tool in our formulation is the Lax pair written by $4\times4$ matrix differential…
The non-topological, stationary and propagating, soliton solutions of the classical continuous Heisenberg ferromagnet equation are investigated. A general, rigorous formulation of the Inverse Scattering Transform for this equation is…
A generalized inhomogeneous higher-order nonlinear Schrodinger (GIHNLS) equation for the Heisenberg ferromagnetic spin chain system in (1+1)-dimensions under zero boundary condition at infinity is taken into account. The spectral analysis…
We analyze several types of soliton solutions to a family of Tzitzeica equations. To this end we use two methods for deriving the soliton solutions: the dressing method and Hirota method. The dressing method allows us to derive two types of…
The Sine-Gordon equation is integrable in (1+1)-dimensional Minkowski and in 2-dimensional Euclidean spaces. In each case, it has a Lax pair, and a Hirota algorithm generates its N soliton solutions for all N greater than or equal to 1. The…