Domain wall and periodic solutions of coupled asymmetric double well models

Abstract

Domain wall and periodic solutions of coupled 4 models in an external fieldCoupled asymmetric double well ͑a 2 − b 3 + c 4 ͒ one-dimensional potentials arise in the context of first order phase transitions both in condensed matter physics and field theory. Here we provide an exhaustive set of exact periodic solutions of such a coupled asymmetric model in terms of elliptic functions ͑domain wall arrays͒ and obtain single domain wall solutions in specific limits. We also calculate the energy and interaction between solitons for various solutions. Both topological ͑kinklike at T = T c ͒ and nontopological ͑pulselike for T T c ͒ domain wall solutions are obtained. We relate some of these solutions to domain walls in hydrogen bonded materials and also in the field theory context. As a by-product, we also obtain a new one parameter family of kink solutions of the uncoupled asymmetric double well model.

Domain wall and periodic solutions of a coupled ϕ6 model

“…In this context, we note that in recent publications we have obtained a large number of periodic solutions, in terms of Lamé polynomials of order one and two, of coupled φ 4 problems, both when the φ 4 potential corresponds to the second as well as to the first order transition [9,10,11]. The obvious question then is whether one can also obtain exact solutions of the coupled φ 6 -φ 4 problems, both when the φ 4 potential corresponds to the second as well as to the first order transition.…”

Mapping between generalized nonlinear Schrödinger equations and neutral scalar field theories and new solutions of the cubic–quintic NLS equation

“…This is done so that one can easily pick up the solutions recently obtained by us in a related paper on coupled φ 2 -φ 3 -φ 4 field theory [9].…”

Novel Superposed Kink and Pulse Solutions for $ϕ^4$, MKdV, NLS and Other Nonlinear Equations

“…But before we proceed further, let us recall the three well known periodic solutions of the asymmetric field Eq. (47) [14,15]. In particular, it is well known that Eq.…”