Related papers: Coupled Sine-Gordon and $\phi^4$ System
We have examined the dynamical behavior of the kink solutions of the one-dimensional sine-Gordon equation in the presence of a spatially periodic parametric perturbation. Our study clarifies and extends the currently available knowledge on…
An integrable two-dimensional system related to certain fermion-soliton systems is studied. The self-consistent solutions of a static version of the system are obtained by using the tau function approach. The self-consistent solutions…
We consider a classical equation known as the $\phi^4$ model in one space dimension. The kink, defined by $H(x)=\tanh(x/{\sqrt{2}})$, is an explicit stationary solution of this model. From a result of Henry, Perez and Wreszinski it is known…
We theoretically study bright and dark solitons in an experimentally relevant hybrid system characterized by strong light-matter coupling. We find that the corresponding two-component model supports a variety of coexisting moving solitons…
We consider the sine-Gordon equation in laboratory coordinates in the quarter plane. The first part of the paper considers the construction of solutions via Riemann-Hilbert techniques. In addition to constructing solutions starting from…
Examining the $\phi^{4}$ and $\phi^{8}$ models within a two-dimensional framework in the flat spacetime and embracing a theory with unconventional kinetic terms, one investigates the emergence of kinks/antikinks and double-kinks/antikinks.…
It was recently noted how the classical sine-Gordon theory can support discontinuities, or `defects', and yet maintain integrability by preserving sufficiently many conservation laws. Since soliton number is not preserved by a defect, a…
Exact particle-like static, spherically and/or cylindrically symmetric solutions to the equations of interacting scalar and electromagnetic field system have been obtained. We considered Freedman-Robertson-Walker (FRW) space-time as an…
A symmetric $\phi^4$-$\phi^2 |\phi|$-$\phi^2$ model has recently attracted a lot of attention due to its usefulness in studying tunable phase transitions. We analyze the behavior of this model for the entire range of parameters and obtain…
We show that $(1+2)$ nonlinear Klein-Gordon equation with negative coupling admits an exact solution which appears to be the linear superposition of the plane wave and the nonsingular rational soliton. We show that the same approach allows…
We present an analytical and numerical study of the Klein-Gordon kink-soliton dynamics in inhomogeneous media. In particular, we study an external field that is almost constant for the whole system but that changes its sign at the center of…
The 4-dimensional effective theory arising from an induced gravity action for a co-dimension greater than one brane consists of multiple galileon fields pi^I, I=1...N, invariant under separate Galilean transformations for each scalar, and…
We study a scalar field model in a two dimensional space-time with a generalized $\phi^4_G$ potential which has four minima, obtaining novel kink solutions with well defined properties although the potential is non-analytical at the origin.…
The fractal velocity pattern in symmetric kink-antikink collisions in $\phi^4$ theory is shown to emerge from a dynamical model with two effective moduli, the kink-antikink separation and the internal shape mode amplitude. The shape mode…
The Euclidean analogues of the sine-Gordon solitons are used as sources of the heterotic fivebrane solutions in the ten-dimensional heterotic string theory. Some properties of these soliton solutions are discussed. These solitons in…
In this article, we study kink soliton configurations in interacting scalar field theories containing two fields without $SO(2)$ invariance. We study a class of such theories, the well-known Montonen-Sarker-Trullinger-Bishop model is one of…
Directed motion of topological solitons (kinks or antikinks) in the damped and AC-driven discrete sine-Gordon system is investigated. We show that if the driving field breaks certain time-space symmetries, the soliton can perform…
We study simultaneous collisions of two, three, and four kinks and antikinks of the $\phi^6$ model at the same spatial point. Unlike the $\phi^4$ kinks, the $\phi^6$ kinks are asymmetric and this enriches the variety of the collision…
The nonlinear Schrodinger equation supports solitons -- self-interacting, localized states that behave as nearly independent objects. We exhibit solitons with self-induced nonreciprocal dynamics in a discrete nonlinear Schrodinger equation.…
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,…