Related papers: Domain Wall and Periodic Solutions of Coupled phi6…
Linear differential equations of arbitrary order with polynomial coefficients are considered. Specifically, necessary and sufficient conditions for the existence of polynomial solutions of a given degree are obtained for these equations. An…
Condsidering a massive self-interacting phi ^6 scalar field coupled arbitrarily to a (2+1) dimensional Bianchi type-I spacetime, we evaluate the one-loop effective potential. It is found that phi ^6 potential can be regularized in (2+1)…
In this article, we investigate the existence and properties of time-periodic solutions for damped evolutionary partial differential equations subject to periodic forcing. Particular emphasis is placed on configurations where the energy…
This work deals with bifurcation and pattern changing in models described by two real scalar fields. We consider generic models with quartic potentials and show that the number of independent polynomial coefficients affecting the ratios…
Domain wall, wormhole, particlelike, and cosmic string general relativistic solutions supported by two interacting phantom or ordinary scalar fields with 4th-, 6th-, and 8th-order potentials are studied. Numerical calculations indicate that…
We study a one-dimensional ordinary differential equation modelling optical conveyor belts, showing in particular cases of physical interest that periodic solutions exist. Moreover, under rather general assumptions it is proved that the set…
Identifying integrable coupled nonlinear ordinary differential equations (ODEs) of dissipative type and deducing their general solutions are some of the challenging tasks in nonlinear dynamics. In this paper we undertake these problems and…
We present here the explicit parametric solutions of second order differential equations invariant under time translation and rescaling and third order differential equations invariant under time translation and the two homogeneity…
We study the existence of a periodic solution for a differential equation with distributed delay. It is shown that, for a class of distributed delay diferential quations, a symmetric period 2 solution, where the period is twice the maximum…
In this paper, we propose an equivariant degree based method to study bifurcation of periodic solutions (of constant period) in symmetric networks of reversible FDEs. Such a bifurcation occurs when eigenvalues of linearization move along…
We consider periodic second-order equations having an ordered pair of lower and upper solutions and show the existence of asymptotic trajectories heading towards the maximal and minimal periodic solutions which lie between them.
We consider (2+1) and (1+1) dimensional long-wave short-wave resonance interaction systems. We construct an extensive set of exact periodic solutions of these systems in terms of Lam\'e polynomials of order one and two. The periodic…
Traditionally, covariant scalar field theory models are either super renormalizable, strictly renormalizable, or nonrenormalizable. The goal of `Mixed Models' is to make sense of sums of these distinct examples, e.g.,…
In this paper we present a new method of solving certain quartic and higher degree homogeneous polynomial diophantine equations in four variables. The method can also be extended to solve simultaneous homogeneous polynomial diophantine…
The full history recursive multilevel Picard approximation method for semilinear parabolic partial differential equations (PDEs) is the only method which provably overcomes the curse of dimensionality for general time horizons if the…
Many new solitary wave solutions of the recently studied Lienard equation are obtained by mapping it to the field equation of the $\phi^6-$field theory. Further, it is shown that the exact solutions of the Lienard equation are also the…
A systematic procedure to derive exact solutions of the associated Lame equation for an arbitrary value of the energy is presented. Supersymmetric transformations in which the seed solutions have factorization energies inside the gaps are…
We construct stable periodic solutions for a simple form nonlinear delay differential equation (DDE) with a periodic coefficient. The equation involves one underlying nonlinearity with the multiplicative periodic coefficient. The well-known…
We give a reformulation of a six-parameter family of coupled Painlev\'e VI systems with affine Weyl group symmetry of type $D_6^{(1)}$ from the viewpoint of its symmetry and holomorphy properties.
We identify two recursively defined polynomial conditions for FI-modules in the literature. We characterize these conditions using homological invariants of FI-modules (namely the local degree and regularity, together with the stable…