arXiv subjects

Prasanta Chatterjee

Publications and source records attributed to Prasanta Chatterjee.

12 recordsLinked to original sources

arXiv2026

Formation and interaction of two-dimensional electron-acoustic solitons and breathers in superthermal plasmas

The nonlinear evolution and mutual interaction of two-dimensional electron acoustic (EA) nonlinear structures in superthermal plasma environment are studied. The plasma model consists of inertial cold electrons, superthermal hot electrons described by kappa ($\kappa$) distribution, and stationary ions providing overall charge neutrality. Using the extended Poincar\'e-Lighthill-Kuo (PLK) reductive perturbation technique, a pair of two-sided Kadomtsev-Petviashvili (KP) equations governing right- and left-propagating EA solitary waves (EASWs) is derived. Exact analytical solutions of the KP equations, including single soliton, multisoliton, breather, and lump structures, are obtained via the Hirota bilinear method. The effects of key plasma parameters such as hot electron concentration, temperature ratio, and superthermality index on the characteristics of these nonlinear excitations are examined. Particular attention is devoted to the head-on collision dynamics between solitons, breather-soliton, and breather-breather interactions. The results reveal quasi-elastic collisions accompanied by phase shifts, transient amplitude modulation, and localized energy concentration, with clear distinctions between oscillatory and non-oscillatory mode interactions. The present study provides new insights into multidimensional electron acoustic wave (EAW) dynamics and energy redistribution mechanisms in superthermal space plasmas, with direct relevance to planetary magnetospheric environments such as Saturn's ring region.

physics.plasm-ph↗

arXiv2026

Non-Local Energy Dissipation and Topological Obstructions in the Second-Order Positive Modified Burgers' Equation

We study the higher-order flows of the modified Burgers' equation generated by its standard recursion operator. In particular, we show that the second-order positive flow takes the form of a non-local integro-differential equation. After reducing the equation to a traveling-wave form, we investigate its asymptotic energy behavior. The resulting analysis shows that the non-local energy flux prevents the formation of both topological kink and bell-shaped solitary waves. We show that the non-local dissipation permanently breaks the asymptotic equilibrium between nonlinear convection and linear dispersion, forcing an irreversible energy imbalance. Our analysis shows that the solitary waves are unstable. The non-local term causes continuous energy loss through radiation. As a result, the traveling wave cannot keep a stable and symmetric shape.

math.AP↗

arXiv2026

Emergence of fractal structures from breather interactions in the $(2+1)$-dimensional Konopelchenko--Dubrovsky equation

Fractal structures generated through nonlinear breather interactions are investigated for the $(2+1)$-dimensional Konopelchenko--Dubrovsky (KD) equation by means of the Hirota bilinear method. The bilinear form of the system is first derived, after which breather interaction solutions are constructed analytically through suitable auxiliary functions. It is shown that the interaction of breather waves in the coupled nonlinear environment gives rise to highly intricate multiscale patterns exhibiting self-similar behaviour under successive magnification. To characterize the geometric complexity of the obtained structures, a three-dimensional voxel-based box-counting method is employed. The computed dimensions are found to be non-integer, confirming the fractal nature of the generated patterns. In addition, relative error analysis, standard error estimation, bootstrap standard deviation and convergence analysis are performed to examine the robustness and reproducibility of the estimated dimensions. The present work suggests that nonlinear breather interactions in coupled dispersive systems may provide a natural mechanism for the emergence of fractal geometries and complex multiscale structures. The combined analytical and quantitative framework developed here may provide further insight into nonlinear energy localization and scale-dependent structures arising in fluid dynamics, plasma physics and nonlinear wave propagation.

math-ph↗

arXiv2026

Exact solution of the (2+1)-dimensional damping forcing coupled Burgers equation by using Darboux transformation

In this article, we investigate the (2+1)-dimensional damping forcing coupled Burgers equation, which is obtain by adding damping and forcing terms from couple Burgers equation. The Lax pair of the (2+1)-dimensional damping forcing coupled Burgers equation is established. With the help of Lax pair, we derive the $N$-fold Darboux transformation of (2+1)-dimensional damping forcing coupled Burgers equation. Using one fold and two fold Darboux transformation, we demonstrated some wave solutions including solitary wave solution and periodic wave solution. The impact of damping and forcing terms in solitary wave solution and periodic solution is graphically demonstrated.

math.AP↗

arXiv2025

Fractal Dimension in Nonlinear Wave Dynamics Governed by a Nonlinear Partial Differential Equation

This work presents a detailed analytical and geometrical investigation of the (2+1)-dimensional Boiti-Leon-Pempinelli system, a nonlinear dispersive model arising in the context of fluid and plasma dynamics. By employing a projective Riccati-based ansatz, a new class of exact solutions is systematically derived. These solutions, when visualized, exhibit intricate geometrical features that evolve across multiple spatial scales. To quantify this complexity, a voxel-based box-counting dimension analysis is conducted on the corresponding surface profiles. The analysis reveals non-integer fractal dimensions that vary with magnification, confirming the self-affine nature of the patterns and highlighting the multiscale structure inherent in the system. Such fractal character is not only of theoretical interest but also reflects real-world behaviors in turbulent plasma flows and fine-scale fluid instabilities. The study thus bridges exact analytical solutions with computational fractal geometry, providing a deeper understanding of the BLP system and its relevance in describing natural phenomena characterized by spatial complexity and multiscale interactions.

math-ph↗

arXiv2025

Characterizing ion-acoustic shock wave collisions in Martian multicomponent plasma environments

We present theoretical investigation of colliding ion-acoustic (IA) shock waves in Martian multicomponent plasmas consisting of hydrogen ($H^+$), oxygen ($O^+$) and oxygen molecule ($O_2^+$) ions, including background superthermal electrons (modeled by a $\kappa$-(kappa) distribution function). A set of Burgers' equations is obtained by adopting a modified Poincar\'e-Lighthill-Kuo (PLK) perturbation method to describe the head-on-collision dynamics of dissipative nonlinear IA wave structures. We have estimated the spatio-temporal scales using parameters typically observed in the Martian atmosphere by the MAVEN spacecraft, for which shock waves are theoretically expected to undergo mutual collisions in the multicomponent plasma. The effects of head-on collisions on the electrostatic potential profiles arising from one-fold and two-fold IA shock interactions are explored. Our numerical analysis reveals that the collision leads to a noticeable broadening of the shock structures with the enhancement of kinematic viscosity.

physics.plasm-ph↗

arXiv2025

Multi-lump, lump-kink and interaction of breather with other nonlinear waves of a couple Boussinesq system

We investigate the interaction characteristics of nonlinear coherent structures in the couple Boussinesq (CB) system using the Hirota bilinear approach. First, we derive the lump solutions using a positive quadratic polynomial within the Hirota perturbation technique. Next, We study the explicit interactions between lumps and one or two-kink waves, and observe double lump patterns. Furthermore, we discover the interactions of breathers, revealing a diffusion-like behavior. We notice that breather waves can interact with periodic, kink, and bright solitons for specific parameter sets in the CB system. Interactions between two chains of double breathers are also found. We analyze our results using a combination of symbolic computations and graphical representations, providing a deeper understanding of their behavior. This study reveals previously unreported nonlinear dynamics in the CB system.

nlin.PS↗

arXiv2024

Analysis of Solitons within the framework of the fractional Zakharov-Kuznetsov equation utilizing Hirota bilinear method

The influence of fractional order parameter $(\alpha)$ in nonlinear waves is examined in the fractional Zakharov-Kuznetsov (FZK) equation with the Hirota bilinear approach. Symbolic computation is used for all mathematical calculations. A significant impact of the fractional order parameter is found on the single and multi-soliton solutions. The fact that the structural change is noticeable when $\alpha$ is raised, is crucial to our investigation.

nlin.PS↗

arXiv2024

Study of Breather Structures in the Framework of Gardner Equation in Electron-Positron-Ion Plasmas

In different nonlinear mediums, the wave trains carry energy and expose many amazing features. To describe a nonlinear phenomenon, a soliton is one that preserves its shape and amplitude even after the collision. Breather is one kind of soliton structure, which is a localized wave that periodically oscillates in amplitude. This article uses the reductive perturbation technique (RPT) to get the GE from a plasma system with four parts: cold positrons that can move, hot positrons and hot electrons that are spread out in a kappa pattern, and positive ions that can't move. Then, using the Hirota bilinear method (HBM), it is possible to obtain the multi-soliton and breather structures of GE. Breathers are fluctuating regional wave packets and significantly participate in hydrodynamics as well as optics; besides, their interaction can alter the dynamical characteristics of the wave fields. We also incorporate a detailed numerical simulation study based on a newly designed code by two of the co-authors. It is found that in our plasma system, soliton solutions, especially breather solutions, exist. Although superthermal (kappa-distributed) electrons and positrons play an important role in soliton structures, This type of analysis can also apply to the propagation of finite-amplitude waves in natural phenomena like the atmosphere, ocean, optic fibres, signal processing, etc. It should also be useful to study different electrostatic disturbances in space and laboratory plasmas, where immobile positive ions, superthermal electrons, superthermal hot positrons, and mobile cold positrons are the major plasma species.

physics.plasm-ph↗

arXiv2023

Nonextensive Effect on the Lump Soliton Structures in Dusty Plasma

In this paper, we use a very prominent technique, Hirota Bilinear Method (HBM) to survey the lump structures of the Kadomtsev-Petviashvili (KP) equation in the frame of a collisionless magnetized plasma system composed of dust grains, ions, and nonextensive electrons. Nonlinearity has worldwide applications, and soliton theory is a powerful appliance to illustrate its qualitative behaviors. So, lump solitons are very significant and also interesting. We have observed that lump structures differ due to the correlated parameters of the plasma system. It has also been found that the nonextensive parameter crucially changes the lump features.

physics.plasm-ph↗

arXiv2021

Effect of dust-ion collision on superthermal plasmas in cylindrical and spherical geometry

Dust-ion collisional effect in dust ion acoustic waves is investigated in the framework of spherical and cylindrical geometry. For such study the fluid equation are takes and collisional effect is consider in the equation of momentum balance. Using reductive perturbation technique the evolution equation is derived with additional damping term for non planner geometry. Using the conservation principle an analytical time dependent solitary wave solution is obtained for the evolution equation. It is seen that dust ion collisional frequency has an significant effect on the width and amplitude of the solitary wave solution.

physics.plasm-ph↗

arXiv2020

Average conservative chaos in quantum dusty plasmas

We consider a hydrodynamic model of a quantum dusty plasma. We prove mathematically that the resulting dust ion acoustic plasma waves present the property of being conservative on average. Furthermore, we test this property numerically, confirming its validity. Using standard techniques from the study of dynamical systems, as for example the Lyapunov characteristic exponents, we investigate the chaotic dynamics of the plasma and show numerically its existence for a wide range of parameter values. Finally, we illustrate how chaotic dynamics organizes in the parameter space for fixed values of the initial conditions, as the Mach number and the quantum diffraction parameter are continuously varied.

physics.plasm-ph↗