Logarithmic potential with super-super-exponential kink profiles and tails
Avinash Khare, Avadh Saxena
Abstract
Abstract We consider a novel one dimensional model of a logarithmic potential which has super-super-exponential kink profiles as well as kink tails. We provide analytic kink solutions of the model—it has 3 kinks, 3 mirror kinks and the corresponding antikinks. While some of the kink tails are super-super-exponential, some others are super-exponential whereas the remaining ones are exponential. The linear stability analysis reveals that there is a gap between the zero mode and the onset of continuum. Finally, we compare this potential and its kink solutions with those of very high order field theories harboring seven degenerate minima and their attendant kink solutions, specifically ϕ 14 , ϕ 16 and ϕ 18 .
Topics & Concepts
PhysicsMaxima and minimaDegenerate energy levelsLogarithmKink instabilityField (mathematics)Stability (learning theory)Work (physics)Order (exchange)Zero (linguistics)Zero modeLogarithmic growthQuantum electrodynamicsMode (computer interface)Classical mechanicsQuantum mechanicsMathematical physicsInstabilityThird orderLine (geometry)Measure (data warehouse)Nonlinear Photonic SystemsNonlinear Waves and SolitonsNonlocal and gradient elasticity in micro/nano structures