Related papers: Asymmetric kink solutions of hyperbolically deform…
The intrinsically relativistic problem of spinless particles subject to a general mixing of vector and scalar kink-like potentials ($\sim \mathrm{tanh} ,\gamma x$) is investigated. The problem is mapped into the exactly solvable…
We consider a complex periodic PT-symmetric potential of the Kronig-Penney type, in order to elucidate the peculiar properties found by Bender et al. for potentials of the form $V=i(\sin x)^{2N+1}$, and in particular the absence of…
Given a kink bearing Hamiltonian, Isospectral Hamiltonian approach is used in generating new sets of Hamiltonains which also admit kink solutions. We use Sine-Gordon model as a example and explicitly work out the new sets of potentials and…
Asymptotic properties of solutions of difference equation of the form \[ \Delta^m(x_n+u_nx_{n+k})=a_nf(n,x_{\sigma(n)})+b_n \] are studied. We give sufficient conditions under which all solutions, or all solutions with polynomial growth, or…
In this work we present some classes of models whose the corresponding two coupled first-order nonlinear equations can be put into a linear form, and consequently be solved completely. In these cases the so-called trial orbit method is…
Inflationary $\alpha$-attractor models can be naturally implemented in supergravity with hyperbolic geometry. They have stable predictions for observables, such as $n_s=1-{2/ N_e} $, assuming that the potential in terms of the original…
We develop a systematic procedure for constructing quantum many-body problems whose spectrum can be partially or totally computed by purely algebraic means. The exactly-solvable models include rational and hyperbolic potentials related to…
Certain supersymmetric sigma models in 2+1 dimensions feature multi-soliton solutions, with and without scattering. We subject these systems to a non-anticommutative deformation by replacing the Grassmann algebra of the odd superspace…
We present a review of our recent works directed towards discovery of a periodic, kink-like and soliton-like travelling wave solutions within the models of transport phenomena and the mathematical biology. Analytical description of these…
In this paper, we employ the bifurcation theory of planar dynamical systems to investigate the traveling wave solutions of a 2-component of the Degasperis-Procesi equation. The expressions for smooth soliton, kink and antikink solutions are…
We study a particular deformation of the potential KdV model (pKdV) and construct the quasi-conservation laws by a direct method. The charge densities, differing from their integrable counterpart with homogeneous degree terms, exhibit mixed…
We study the evolution of fronts in the Klein-Gordon equation when the nonlinear term is non-homogeneous. Extending previous works on homogeneous nonlinear terms, we describe the derivation of an equation governing the front motion, which…
We consider the interaction of solitons in a biharmonic, beam model analogue of the well-studied $\phi^4$ Klein-Gordon theory. Specifically, we calculate the force between a well separated kink and antikink. Knowing their accelerations as a…
We investigate the dynamics of the kinks that emerge in a one-dimensional scalar field theory with an octic potential containing a quartic minimum and two quadratic minima. We show analytically that kink-antikink and kink-kink pairs…
The relativistic problem of spin- fermions subject to vector hyperbolic (kink-like) potential tanh (kx) is investigated by using the parametric Nikiforov-Uvarov method. The energy eigenvalue equation and the corresponding normalized wave…
We investigate a (1+1)-dimensional nonlinear field theoretic model with the field potential $V(\phi)| = |\phi|.$ It can be obtained as the universal small amplitude limit in a class of models with potentials which are symmetrically V-shaped…
We describe the kink solitary waves of a massive non-linear sigma model with an ${\mathbb S}^2$ sphere as the target manifold. Our solutions form a moduli space of non-relativistic solitary waves in the long wavelength limit of…
Many solitonic configurations in field theory have localized bound states in their spectrum of linear perturbations. This opens up the possibility of having long lived excitations of these solitons that could affect their dynamics. We start…
The construction of analytic solutions for quasi-exactly solvable systems is an interesting problem. We revisit a class of models for which the odd solutions were largely missed previously in the literature: the anharmonic oscillator, the…
We consider non-topological, "bell-shaped" localized and regular solutions available in some 1+1 dimensional scalar field theories. Several properties of such solutions are studied, namely their stability and the occurence of fermion bound…