Narrow Results

Wigner distributions play a significant role in formulating the phase–space analog of quantum mechanics. The Schrödinger wave functional for solitons is needed to derive it for solitons. The Wigner distribution derived can further be used for calculating the charge distributions, current densities and wave function amplitude in position or momentum space. It can be also used to calculate the upper bound of the quantum speed limit time. We derive and analyze the Wigner distributions for Kink and Sine-Gordon solitons by evaluating the Schrödinger wave functional for both solitons. The charge, current density, and quantum speed limit for solitons are also discussed which we obtain from the derived analytical expression of Wigner distributions.

We study DNA dynamics relying on the plane-base rotator model for DNA. It is shown that this dynamics can be represented by kink and antikink solitons. We demonstrate that two velocities are relevant and these are the velocities of both a double and a single stranded DNA. A key question is which one is bigger as this is related to a value of the ratio of two parameters describing the hydrogen and the covalent interactions in DNA. If the velocity of double stranded DNA is larger than one of the single stranded chain then the two ferromagnetic strands are coupled antiferromagnetically. Otherwise, the two DNA strands are coupled ferromagnetically. We discuss possible experiments based on micromanipulation techniques that should be carried out to determine these velocities and the solitonic width.

In this paper, several types of solitons such as dark soliton, bright soliton, periodic soliton, kink soliton and solitary waves in three-dimensional and two-dimensional contour plot have been derived for the generalized third-order nonlinear Schrödinger dynamical equations (NLSEs). The generalized third-order NLSE is a significant model ultra-short pulses in optical fibers. The computational work and outcomes achieved show the influence and efficiency of current method. Furthermore, we can solve many other higher-order NLSEs with the help of simple and effective technique.

We investigated the soliton behavior in one-dimensional Bose–Einstein condensates. Based on the modified Gross–Pitaevskii equation (GPE) model with higher-order nonlinear interaction and through the F-expansion method, we derived the analytical kink soliton solution of the one-dimensional GPE. The typical kink soliton features under the specific experimental setting are identified, and the physical implication of the analytical results is also demonstrated. The derived theoretical results can be used to guide the experimental study of kink soliton in ultracold atomic systems with higher-order nonlinearity.