Related papers: Soliton solutions in two-dimensional Lorentz-viola…
We use a description based on differential forms to systematically explore the space of scalar-tensor theories of gravity. Within this formalism, we propose a basis for the scalar sector at the lowest order in derivatives of the field and…
Equations of motion for a classical 3d discrete model, whose auxialiary system is a linear system, are investigated. The Lagrangian form of the equations of motion is derived. The Lagrangian variables are a triplet of "tau functions". The…
Starting from lagrangian field theory and the variational principle, we show that duality in equations of motion can also be obtained by introducing explicit spacetime dependence of the lagrangian. Poincare invariance is achieved precisely…
We discuss an elementary derivation of variational symmetries and corresponding integrals of motion for the Lagrangian systems depending on acceleration. Providing several examples, we make the manuscript accessible to a wide range of…
The purpose of this article is to initiate a study of a class of Lorentz invariant, yet tractable, Lagrangian Field Theories which may be viewed as an extension of the Klein-Gordon Lagrangian to many scalar fields in a novel manner. These…
As an alternative to the covariant Ostrogradski method, we show that higher-derivative relativistic Lagrangian field theories can be reduced to second differential-order by writing them directly as covariant two-derivative theories…
We investigate a class of gravity theories respecting only spatial covariance, termed spatially covariant gravity, in the presence of an auxiliary scalar field. We examine the conditions on the Lagrangian required to eliminate scalar…
In general, the system of $2$nd-order partial differential equations made of the Euler-Lagrange equations of classical field theories are not compatible for singular Lagrangians. This is the so-called second-order problem. The first aim of…
We calculate soliton solutions to the scalar field equation of motion that arises for the 4th-order extended Lagrangian (\(\phi^{4}\) theory) in quantum field theory using the extended hyperbolic tangent and the sine-cosine methods. Using…
Ostrogradsky instability generally appears in nondegenerate higher-order derivative theories and this issue can be resolved by removing any existing degeneracy present in such theories. We consider an action involving terms that are at most…
In this paper we consider a class of systems of two coupled real scalar fields in bidimensional spacetime, with the main motivation of studying classical or linear stability of soliton solutions. Firstly, we present the class of systems and…
We study static kink configurations in a type of two-dimensional higher derivative scalar field theory whose Lagrangian contains second-order derivative terms of the field. The linear fluctuation around arbitrary static kink solutions is…
We revisit the problem of building the Lagrangian of a large class of metric theories that respect spatial covariance, which propagate at most two degrees of freedom and in particular no scalar mode. The Lagrangians are polynomials built of…
Lagrangian motions of fluid particles in a general velocity field oscillating in time are studied with the use of the two-timing method. Our aims are: (i) to calculate systematically the most general and practically usable asymptotic…
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…
In this work, we present a consistent Hamiltonian analysis of cosmological perturbations at all orders. To make the procedure transparent, we consider a simple model and resolve the `gauge-fixing' issues and extend the analysis to scalar…
Higher order derivative theories, generally suffer from instabilities, known as Ostrogradsky instabilities. This issue can be resolved by removing any existing degeneracy present in such theories. We consider a model involving at most…
Scalar-tensor theories are one of the most natural and well-constrained alternative theories of gravity, while still allowing for significant deviations from general relativity. We present the equations of motion of nonspinning compact…
New, gauge-independent, second-order Lagrangian for the motion of classical, charged test particles is proposed. It differs from the standard, gauge-dependent, first order Lagrangian by boundary terms only. A new method of deriving…
The scalar normal modes of higher dimensional gravitating kink solutions are derived. By perturbing to second order the gravity and matter parts of the action in the background of a five-dimensional kink, the effective Lagrangian of the…