We explore the quench dynamics of a binary Bose-Einstein condensate crossing the miscibility-immiscibility threshold and vice versa, both within and in particular beyond the mean-field approximation. ...Increasing the interspecies repulsion leads to the filamentation of the density of each species, involving shorter wavenumbers and longer spatial scales in the many-body (MB) approach. These filaments appear to be strongly correlated and exhibit domain-wall structures. Following the reverse quench process multiple dark-antidark solitary waves are spontaneously generated and subsequently found to decay in the MB scenario. We simulate single-shot images to connect our findings to possible experimental realizations. Finally, the growth rate of the variance of a sample of single-shots probes the degree of entanglement inherent in the system.
In this note, we characterize Sasakian manifolds endowed with ∗-η-Ricci-Yamabe solitons. Also, the existence of ∗-η-Ricci-Yamabe solitons in a 5-dimensional Sasakian manifold has been proved through ...a concrete example.
In this study, an effort has been made to obtain optical soliton solutions of the (1+1)-dimensional Biswas-Milovic equation
which was introduced by Biswas and Milovic in 2010, having Kerr law and ...parabolic-law with weak non-local nonlinearity in the
presence of spatio-temporal dispersion, which is one of the important models for nonlinear optics. Although, the model is an equation
that has been studied by many researchers, the fact that the form to be examined has not been studied before. As a general algorithm,
first converting the model to nonlinear ordinary differential form with a complex wave transformation, then obtaining candidate optical
soliton solutions by utilizing the new Kudryashov technique, determining the ones that satisfy the main equation from these solutions
as the exact solution, and in order to better understand the obtained solutions by making graphical presentation and providing the
necessary comments constitute the main framework of the article.
In this study, an effort has been made to obtain optical soliton solutions of the (1+1)-dimensional Biswas-Milovic equation
which was introduced by Biswas and Milovic in 2010, having Kerr law and parabolic-law with weak non-local nonlinearity in the
presence of spatio-temporal dispersion, which is one of the important models for nonlinear optics. Although, the model is an equation
that has been studied by many researchers, the fact that the form to be examined has not been studied before. As a general algorithm,
first converting the model to nonlinear ordinary differential form with a complex wave transformation, then obtaining candidate optical
soliton solutions by utilizing the new Kudryashov technique, determining the ones that satisfy the main equation from these solutions
as the exact solution, and in order to better understand the obtained solutions by making graphical presentation and providing the
necessary comments constitute the main framework of the article.
This study explores the soliton solutions for the perturbed Radhakrishnan-Kundu-Lakshmanan (RKL) equation which
includes M-truncated derivative. Initially, a wave transformation technique is employed ...for the RKL equation, yielding a nonlinear
ordinary differential equation (NODE). Then, the NODE is solved using the new Kudryashov method. A candidate solution and its
related derivatives are incorporated into the NODE, resulting in a polynomial expression. A system of algebraic equations emerges by
equating coefficients of terms with similar degrees to zero. Solving this system provides the identification of unknown variables in the
candidate solution, thereby yielding the solutions to the RKL equation. Diverse illustrations of the obtained solutions are presented via
contour, two-dimensional, and three-dimensional plots. The findings of this research may present potential implications for future
studies in nonlinear optics.
This study explores the soliton solutions for the perturbed Radhakrishnan-Kundu-Lakshmanan (RKL) equation which
includes M-truncated derivative. Initially, a wave transformation technique is employed for the RKL equation, yielding a nonlinear
ordinary differential equation (NODE). Then, the NODE is solved using the new Kudryashov method. A candidate solution and its
related derivatives are incorporated into the NODE, resulting in a polynomial expression. A system of algebraic equations emerges by
equating coefficients of terms with similar degrees to zero. Solving this system provides the identification of unknown variables in the
candidate solution, thereby yielding the solutions to the RKL equation. Diverse illustrations of the obtained solutions are presented via
contour, two-dimensional, and three-dimensional plots. The findings of this research may present potential implications for future
studies in nonlinear optics.
In the present study, we focus on obtaining the optical soliton solutions of the Drinfeld-Sokolov-Satsuma-Hirota (DSSH)
equation using Kudryhashov methods. First, a wave transformation is applied to ...the DSSH equation, resulting in a nonlinear ordinary
differential equation (NLODE). A balance number is deduced through the balancing of this NLODE. Subsequently, candidate solutions,
inclusive of their respective derivatives and the wave transformation, are inserted into the DSSH equation. This results in an equation
in polynomial form. Terms with equal power are grouped together in the new equation, and their coefficients are set to zero, leading
to a system of algebraic equations. Solving this algebraic system facilitates the identification of undetermined parameters within the
candidate solutions, thus yielding the solutions for the DSSH equation. Visualization of these solutions is executed through contour
plots as well as two- and three-dimensional graphical representations. The contributions of this study are of substantial relevance for
subsequent research in nonlinear science.
In the present study, we focus on obtaining the optical soliton solutions of the Drinfeld-Sokolov-Satsuma-Hirota (DSSH)
equation using Kudryhashov methods. First, a wave transformation is applied to the DSSH equation, resulting in a nonlinear ordinary
differential equation (NLODE). A balance number is deduced through the balancing of this NLODE. Subsequently, candidate solutions,
inclusive of their respective derivatives and the wave transformation, are inserted into the DSSH equation. This results in an equation
in polynomial form. Terms with equal power are grouped together in the new equation, and their coefficients are set to zero, leading
to a system of algebraic equations. Solving this algebraic system facilitates the identification of undetermined parameters within the
candidate solutions, thus yielding the solutions for the DSSH equation. Visualization of these solutions is executed through contour
plots as well as two- and three-dimensional graphical representations. The contributions of this study are of substantial relevance for
subsequent research in nonlinear science.
This aim of this paper is revealing the optical soliton solutions of the perturbed quintic Gerdjikov-Ivanov equation, which
models optical soliton transmission in the photonic crystal fibers and ...optical fibers. With the aid of the new Kudryashov scheme, we
successful achieved the bright and dark solitons and we simulated their graphical presentation.
This aim of this paper is revealing the optical soliton solutions of the perturbed quintic Gerdjikov-Ivanov equation, which
models optical soliton transmission in the photonic crystal fibers and optical fibers. With the aid of the new Kudryashov scheme, we
successful achieved the bright and dark solitons and we simulated their graphical presentation.
Abstract
We used the sine-Gordon expansion method to find kink solutions of the Oskolkov equation. A solution can be found by matching coefficients and choosing some parameters of the series. We ...found two possible solutions—one is kink and the other is a hybrid of kink and pulse solitons. These solutions can be used for further studies, such as their stability or their interaction. Specific parameters from the solution could be useful for controlling the physical behavior of a system governed by the Oskolkov equation.
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