arXiv subjects

Rajib Mia

Publications and source records attributed to Rajib Mia.

5 recordsLinked to original sources

arXiv2026

Qualitative analysis, chaotic structure and exact solution of the nonlinear seventh-order Caudrey-Dodd-Gibbon-KP equation

The main objective of this work is to investigate the traveling wave solution and dynamic characteristics of the (2 + 1)-dimensional seventh-order Caudrey-Dodd-Gibbon-KP (sCDG-KP) equation. Applying the ($\frac{G^{\prime}}{G^{\prime}+G+A}$) method, we examine the exact solution of the (2 + 1)-dimensional seventh-order Caudrey-Dodd-Gibbon-KP (sCDG-KP) equation by altering it into a reduced ODE via a suitable wave transformation. Graphical representations, such as 2D, 3D, and a heat map of the ascertained solution, are present to facilitate comprehension of the empirical relevance of the obtained solutions. As a result, we acquired a bright and anti-kink soliton solution. Next, we alter the ODE into a 2D system of equations to analyze the dynamical behavior of the reduced system via bifurcation analysis, phase portrait, and attractor analysis. During this process, we portray the graphical visualization of the bifurcation phase portrait, 2D phase portrait, 3D phase portrait, time series, chaotic attractor, sensitive analysis, fractal dimension, recurrence plot, and power spectrum of the dynamical system.

math.DS↗

arXiv2024

Novel analytical solutions to a new formed model of the (2+1)-dimensional BKP equation using a novel expansion technique

In this article, we present a comprehensive analytical study to obtain the exact traveling wave solutions to a new formed model of the (2+1)-dimensional BKP equation. We construct exact solutions of the considered model using a recently developed expansion technique. This current proposed technique has been successfully implemented to obtain a few exact solutions of a new formed (2+1)-dimensional BKP equation. In order to understand the physical interpretation of solutions effectively, the 2D and 3D graphs are plotted for each type of the solutions obtained for different particular values of the parameters. Furthermore, it is found that the obtained solutions are periodic and solitary wave solutions. We anticipate that the proposed method is reliable and can be applied for obtaining wave solutions of the other nonlinear evolution equations (NLEEs).

math-ph↗

arXiv2024

New exact solutions to the generalized shallow water wave equation

In this work, we study the generalized shallow water wave equation to obtain novel solitary wave solutions. The application of this non-linear model can be found in tidal waves, weather simulations, tsunami prediction, river and irrigation flows, etc. To obtain the new exact solutions of the considered model, we have applied a novel analytical technique namely $\left(\frac{G'}{G'+G+A}\right)$--expansion method. Using the aforementioned method and computational software, we have obtained different kinds of periodic and singular solitary wave solutions of the generalized shallow water wave equation. The obtained solutions are exponential function and trigonometric function solutions. Using 2-D and 3-D plots of the wave solutions, the dynamic behaviors of the developed solutions are displayed. The retrieved solutions validated the effectiveness and robustness of the proposed technique.

math-ph↗

arXiv2016

Stability and Fourier-series periodic solution in the binary stellar systems

In this paper, we use the restricted three body problem in the binary stellar systems, taking photogravitational effects of both the stars. The aim of this study is to investigate the motion of the infinitesimal mass in the vicinity of the Lagrangian points. We have computed semi-analytical expressions for the locations of the collinear points with the help of the perturbation technique. The stability of the triangular points is studied in stellar binary systems Kepler-34, Kepler-35, Kepler-413 and Kepler-16. To investigate the stability of the triangular points, we have obtained the expressions for critical mass which depends on the radiation of both primaries. Fourier-series method is applied to obtain periodic orbits of the infinitesimal mass around triangular points in binary stellar systems. We have obtained Fourier expansions of the periodic orbits around triangular points upto third order terms. A comparison is made between periodic orbits obtained by Fourier-series method and with Runge-Kutta integration of fourth order.

astro-ph.SR↗

arXiv2016

Orbital Dynamics of Exoplanetary Systems Kepler-62, HD 200964 and Kepler-11

The presence of mean-motion resonances (MMRs) in exoplanetary systems is a new exciting field of celestial mechanics which motivates us to consider this work to study the dynamical behaviour of exoplanetary systems by time evolution of the orbital elements of the planets. Mainly, we study the influence of planetary perturbations on semimajor axis and eccentricity. We identify $(r+1):r$ MMR terms in the expression of disturbing function and obtain the perturbations from the truncated disturbing function. Using the expansion of the disturbing function of three-body problem and an analytical approach, we solve the equations of motion. The solution which is obtained analytically is compared with that of obtained by numerical method to validate our analytical result. In this work, we consider three exoplanetary systems namely Kepler-62, HD 200964 and Kepler-11. We have plotted the evolution of the resonant angles and found that they librate around constant value. In view of this, our opinion is that two planets of each system Kepler-62, HD 200964 and Kepler-11 are in 2:1, 4:3 and 5:4 mean motion resonances, respectively. Keywords:astrometry - celestial mechanics - planetary systems.

astro-ph.EP↗