Kundu Mukherjee Naskar Research Articles

Riemann–Hilbert approach for a (2+1) dimensional Kundu–Mukherjee–Naskar equation

Riemann–Hilbert approach for a (2+1) dimensional Kundu–Mukherjee–Naskar equation

Dynamic behavior of explicit elliptic and quasi periodic-wave solutions to the generalized [formula omitted]-dimensional Kundu–Mukherjee–Naskar equation

This paper introduces novel explicit traveling solutions to the generalized (2+1)-dimensional Kundu–Mukherjee–Naskar equation, a model relevant in optical fiber pulses, fluid dynamics, medical imaging, and ocean rogue waves. We propose rational form functions that incorporate both sine and cosine variables or sinh and cosh variables as potential solutions to the model. Subsequently, we utilize 3D diagrams to visually illustrate the characteristics of the identified propagating solutions, which exhibit elliptic-periodic, convex-periodic, cusp-soliton, and quasi-periodic patterns. Furthermore, a graphical analysis is conducted to explore the impact of the model’s parameters; nonlinearity and dispersion. Additionally, we introduce a comparative analysis to assess the superiority of the proposed approach over other existing methods such as Kudryashov-expansion, sine-function, and tanh(coth)-expansion methods. We anticipate that the insights gained from this analysis will prove valuable for understanding and studying other nonlinear models.

Modulations of Stochastic Modeling in the Structural and Energy Aspects of the Kundu–Mukherjee–Naskar System

Modulations of Stochastic Modeling in the Structural and Energy Aspects of the Kundu–Mukherjee–Naskar System

Applying a transformation-based method to extract optical traveling waves from the Kundu–Mukherjee–Naskar equation

Optical solitons are solitary waves that propagate without changing shape due to a balance between dispersion and nonlinearity in the medium. Therefore, solitary optical waves are important solutions to nonlinear partial differential equations for modeling pulse propagation in optics. Our work derives new solitary wave solutions to the Kundu–Mukherjee–Naskar (KMN) equation, which governs complex nonlinear optical wave phenomena. Using innovative logarithmic transformation-based analytical techniques, various solution forms are obtained and expressed in closed form via elementary functions. The solutions are validated through direct substitution into the original KMN equation. Our new solutions provide fresh perspectives into the intricate soliton landscape described by this model. Since the KMN equation finds use in fiber optic communications, fluid dynamics, and other domains, these findings have broad implications. The methods showcase promising new pathways for unraveling soliton behaviors by fractional- and integer-order nonlinear models alike. Researchers can build upon these techniques to further advance understanding of the profound mathematical structures underlying real-world physical systems.

Traveling Wave Optical Solutions for the Generalized Fractional Kundu–Mukherjee–Naskar (gFKMN) Model

The work considers traveling wave optical solutions for the nonlinear generalized fractional KMN equation. This equation is considered for describing pulse propagation in optical fibers and communication systems using two quite similar approaches, based on the expansion of these solutions in the exponential or polynomial forms. Both approaches belong to the direct solving class of methods for PDEs and suppose the use of an auxiliary equation. The solutions acquired in this paper are obtained from first- and second-order differential equations that act as auxiliary equations. In addition, we generated 3D, contour, and 2D plots to illustrate the characteristics of the obtained soliton solutions. To create these plots, we carefully selected appropriate values for the relevant parameters.

Stability analysis and novel optical pulses to Kundu–Mukherjee–Naskar model in birefringent fibers

The concern of this study is to investigate the optical solitons pluses. The [Formula: see text]-dimensional Kundu–Mukherjee–Naskar (KMN) mathematical model in birefringent fibers is taken under consideration for this sake because this model has great importance in optics and delineate the propagation of soliton dynamics in optical fiber communication system and the rogue waves in the oceans and the bending of the light beam. Two newly developed approaches first extended rational sinh-Gordon method which is formulated from the well-known sinh-Gordon equation and second [Formula: see text]-expansion function method are manipulated for the construction of optical solitons in distinct formats. Bright, dark, and singular along their combined forms, periodic and plane wave solutions are extracted with the aid of proposed methods. Moreover, the modulation instability of investigated model is also carried out via linear stability theory. To endorse the physical compatibility of the results, the 2D, 3D, contour, and density plots have been delineated using appropriate parametric values. According to our literature research, these two methods that we are working on have not been applied to the KMN equation in birefringent fibers before, and we believe that the new solutions we have obtained will be useful to researchers working in modeling in this field. The evaluated results suggested that the techniques employed in this research to recover inclusive and standard solutions are approachable, efficient, and speedier in computing and can be considered a handy tool in solving more complex phenomena with the assistance of symbolic computation.

Optical solitons and exact solutions of the (2+1) dimensional conformal time fractional Kundu-Mukherjee-Naskar equation via novel extended techniques

The current work uses a (2+1) dimensional conformal time fractional Kundu-Mukherjee-Naskar (KMN) model to investigate optical soliton transmission across an optical fiber that maintains polarization. Three constructive techniques, namely, the extended power series solution, the new generalized method, and the extended sinh-Gordon expansion method are utilized to find the exact soliton solutions of this model. The invariant analysis has been performed on the (2+1) dimensional time fractional KMN model by using the conformal time fractional derivative. The symmetries obtained using conformal fractional derivative are compared with the symmetries obtained for integer order KMN model because symmetries using Riemann Liouville fractional derivative turned out to be trivial. The given system of fractional PDEs has been reduced by using differential invariants obtained from various linear combinations of vector fields associated with the infinitesimal generator of symmetry transformations. These reduced systems of equations are then investigated for their exact solutions.

Chaotic pattern, bifurcation, sensitivity and traveling wave solution of the coupled Kundu–Mukherjee–Naskar equation

In this paper, the coupled Kundu–Mukherjee–Naskar equation is considered, which is usually used to describe the oceanic rogue waves, hole waves and Bragg grating fibers. Firstly, the traveling wave transformation is applied to convert the coupled Kundu–Mukherjee–Naskar equation into two-dimensional planar dynamic system. Secondly, bifurcation and two-dimensional phase portrait of the coupled Kundu–Mukherjee–Naskar equation are discussed by using the plane dynamics system. What is more, after adding periodic perturbation term, two-dimensional phase portrait, three-dimensional phase portrait, Poincaré section and sensitivity of its perturbed system are plotted by the Maple software. Finally, the optical soliton solutions of the coupled Kundu–Mukherjee–Naskar equation are obtained by using planar dynamical system method.

Application of the generalized unified method to solve (2+1)-dimensional Kundu–Mukherjee–Naskar equation

Application of the generalized unified method to solve (2+1)-dimensional Kundu–Mukherjee–Naskar equation

Optical solitons for Kundu–Mukherjee–Naskar equation via enhanced modified extended tanh method

Optical solitons for Kundu–Mukherjee–Naskar equation via enhanced modified extended tanh method

Exploring new features for the (2+1)-dimensional Kundu–Mukherjee–Naskar equation via the techniques of ($$G^{\prime }/G,1/G$$)-expansion and exponential rational function

Exploring new features for the (2+1)-dimensional Kundu–Mukherjee–Naskar equation via the techniques of ($$G^{\prime }/G,1/G$$)-expansion and exponential rational function

Diverse optical soliton solutions to the Kundu-Mukherjee-Naskar equation via two novel techniques

In this work, the Kundu-Mukherjee-Naskar (KMN) equation that addresses the optical soliton dynamics in (2 +1)-dimensions is studied via two novel techniques, which are the Cole-Hopf transform based method and Wang’s direct mapping method for the first time. Firstly, based on the Cole-Hopf transform, the symbolic computation with the ansatz function schemes are employed to construct the abundant soliton solutions. Some new soliton solutions including the rational breathe, cross-periodic, multi-wave, double exponential form and interaction soliton solutions are obtained. Secondly, Wang’s direct mapping method is adopted to seek for the breather, bright-dark and kinky periodic soliton solutions. Meanwhile, the behaviors of the different soliton solutions are presented in the form of 3-D plot, 2-D contour and 2-D curve. The ideas in this work are expected to provide some new enlightenment for the study of the exact soliton solutions of the PDEs in the optics.

Impacts of nonlinearity and wave dispersion parameters on the soliton pulses of the (2+1)-dimensional Kundu–Mukherjee–Naskar equation

In this study, we explain the impacts of nonlinearity and wave dispersion parameters on the soliton pulses of the (2+1)-dimensional Kundu–Mukherjee–Naskar equation (KMNE). In this regard, some new optical solitons are received via the unified method to the aforesaid equation to explain such impacts of the soliton pulses. The presenting optical solitons are expressed by the dark, periodic, bell, bright, kink, and singular soliton solutions. Taking into account the two impacts help stabilize the soliton pulses during their propagation by generating new dynamics depending upon the nonlinearity and the wave dispersion parameters of the studied equation. All the characteristics of the soliton pulses are exhibited graphically. It is found from the graphical outputs that the soliton profiles are decreasing and increasing with the increase of nonlinearity and dispersion parameters, respectively. The outcomes reveal that the soliton pulses are balanced due to the influences of nonlinearity and wave dispersion parameters of the aforementioned equation. It is mentioned that the impact of wave dispersion and nonlinearity parameters on the soliton pulses has not been discussed in the past. Therefore, the applied method permits the explanation of the various wave dynamics by analyzing the attained soliton solutions in nonlinear optical fibers systems, which can be used for further studies.

Bending of optical solitonic beams modeled by coupled KMN equation

The dynamics of (2 + 1) dimensional optical solitonic beams modeled by coupled Kundu Mukherjee Naskar (KMN) equation are discussed by deriving one bright and one dark soliton solution. The arbitrary bending of solitonic beams of this coupled system has been described by exact curved soliton solutions having an arbitrary function. Such exact analytical results on the bending of solitonic pulse in a bimodal optical fiber system may pave new research directions in this field.

Chirped solitary and traveling wave solutions for the Kundu–Mukherjee–Naskar equation using the Jacobi elliptic function expansion method

Chirped solitary and traveling wave solutions for the Kundu–Mukherjee–Naskar equation using the Jacobi elliptic function expansion method

Optical soliton solution analysis for the (2+1) dimensional Kundu–Mukherjee–Naskar model with local fractional derivatives

Optical soliton solution analysis for the (2+1) dimensional Kundu–Mukherjee–Naskar model with local fractional derivatives

Extraction of some optical solutions to the (2+1)-dimensional Kundu–Mukherjee–Naskar equation by two efficient approaches

The Kundu–Mukherjee–Naskar (KMN) model is considered for describing the pulse propagation in optical fibres and communication systems. Two efficient approaches via the exp (−φ(ξ))-expansion and the improved F-expansion schemes are applied to the KMN model and in order to convert the KMN equation to an ODE, we test the complex wave conversions and present some optical soliton solutions, which are expressed in terms of hyperbolic, rational and trigonometric functions. We create three dimensional and two-dimensional images to explain the underlying optical wave properties of the KMN equation and compare our solutions with the ones in the literature. Our example shows that the two adopted methods provide an efficient mathematical tool for constructing new optical wave solutions to nonlinear partial differential equations arising in fibre optic communication systems.

New Optical Solitons in Bragg Grating Fibers for the Nonlinear Coupled ( 2 + 1 )-Dimensional Kundu-Mukherjee-Naskar System via Complete Discrimination System Method

In this paper, the coupled Kundu-Mukherjee-Naskar (KMN) model in Bragg grating fibers is considered to retrieve some new optical soliton solutions in ( 2 + 1 ) dimensions. Plenty of new exact solutions, including rational function solutions and triangle function solutions, in addition to the Jacobian elliptic function solutions, are obtained by using a complete discrimination system method. The 3D-surface plots, 2D-shape plots, and corresponding 2D contour plots of some obtained solutions are drawn, which provides a visualized structures and propagation of solitons. The novel results are new and show the effectiveness of the proposed method.

Optical solitons to the Kundu–Mukherjee–Naskar equation in (2+1)-dimensional form via two analytical techniques

The current research is about the optical solitons of the Kundu–Mukherjee–Naskar (KMN) equation that are obtained by implementing the two proficient approaches named: the extended Jacobi’s elliptic expansion function method and the expa function method. The aforesaid methods are used for the first time in the KMN equation to obtain novel soliton solutions in terms of Jacobi’s elliptic function solutions, which turn into dark, bright, and periodic solutions later. Also, the rational function solutions of the above-mentioned equation are obtained. The obtained solutions are also graphed and verified with the use of symbolic soft computations. The obtained results may be applied to illustrate the substantial concept of the studious structures as well as other related nonlinear physical structures.

The Optical Solutions of the Stochastic Fractional Kundu–Mukherjee–Naskar Model by Two Different Methods

In this paper, we focus on the stochastic fractional Kundu–Mukherjee–Naskar equation perturbed in the Stratonovich sense by the multiplicative Wiener process. To gain new elliptic, rational, hyperbolic and trigonometric stochastic solutions, we use two different methods: the Jacobi elliptic function method and the (G′/G)-expansion method. Because of the significance of the Kundu-Mukherjee equation in a magnetized plasma, the obtained solutions are useful in understanding many remarkable physical phenomena. Furthermore, we show the effect of the multiplicative Wiener process on the obtained solutions of the Kundu–Mukherjee–Naskar equation.