With the continuous development of society and the increasingly fierce competition among enterprises, it is necessary to analyze the production and operation conditions of enterprises in a timely and effective manner. In the context of the development of information technology, many companies analyze financial data, and corporate financial analysis indicators are the analysis of various report data of the company’s operations, which can effectively reflect the company’s debt repayment, operation, profit, and development capabilities. Enterprises can judge the operation status of the enterprise and make strategic changes in time according to the indicators of enterprise financial analysis. However, due to the large amount of operational data of enterprises and different relationships among different types of data, the analysis of enterprise financial data is not accurate enough when using traditional enterprise financial analysis indicators for analysis. This paper established an engineering scientific model through fuzzy sets and improved the data analysis ability of enterprise financial analysis indicators in enterprises by means of fuzzy analysis. By comparing the enterprise financial analysis indicators of the engineering science model based on fuzzy sets and the traditional enterprise financial analysis indicators, the experimental results showed that the average financial information analysis accuracy of the enterprise financial analysis index based on the engineering science model based on fuzzy sets and the traditional enterprise financial analysis index are 84% and 74%, respectively. Therefore, applying the engineering science model based on fuzzy sets to the corporate financial analysis indicators can effectively improve the accuracy of financial information analysis.
{"title":"Application of Engineering Science Model Based on Fuzzy Sets in Enterprise Financial Evaluation Index","authors":"Yue Wang","doi":"10.1155/2023/5822589","DOIUrl":"https://doi.org/10.1155/2023/5822589","url":null,"abstract":"With the continuous development of society and the increasingly fierce competition among enterprises, it is necessary to analyze the production and operation conditions of enterprises in a timely and effective manner. In the context of the development of information technology, many companies analyze financial data, and corporate financial analysis indicators are the analysis of various report data of the company’s operations, which can effectively reflect the company’s debt repayment, operation, profit, and development capabilities. Enterprises can judge the operation status of the enterprise and make strategic changes in time according to the indicators of enterprise financial analysis. However, due to the large amount of operational data of enterprises and different relationships among different types of data, the analysis of enterprise financial data is not accurate enough when using traditional enterprise financial analysis indicators for analysis. This paper established an engineering scientific model through fuzzy sets and improved the data analysis ability of enterprise financial analysis indicators in enterprises by means of fuzzy analysis. By comparing the enterprise financial analysis indicators of the engineering science model based on fuzzy sets and the traditional enterprise financial analysis indicators, the experimental results showed that the average financial information analysis accuracy of the enterprise financial analysis index based on the engineering science model based on fuzzy sets and the traditional enterprise financial analysis index are 84% and 74%, respectively. Therefore, applying the engineering science model based on fuzzy sets to the corporate financial analysis indicators can effectively improve the accuracy of financial information analysis.","PeriodicalId":49111,"journal":{"name":"Advances in Mathematical Physics","volume":" ","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48118868","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we investigate the stability of set differential equations in Fréchet space F . Some comparison principles and stability criteria are established for set differential equations with the fact that every Fréchet space F is a projective limit of Banach spaces.
{"title":"Stability of Set Differential Equations in Fréchet Spaces","authors":"Junyan Bao, Wei Chen, Peiguang Wang","doi":"10.1155/2023/5134374","DOIUrl":"https://doi.org/10.1155/2023/5134374","url":null,"abstract":"In this paper, we investigate the stability of set differential equations in Fréchet space \u0000 \u0000 F\u0000 \u0000 . Some comparison principles and stability criteria are established for set differential equations with the fact that every Fréchet space \u0000 \u0000 F\u0000 \u0000 is a projective limit of Banach spaces.","PeriodicalId":49111,"journal":{"name":"Advances in Mathematical Physics","volume":" ","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45126632","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Convolution representation manifests itself as an important tool in the reduction of partial differential equations. In this study, we consider the convolution representation of traveling pulses in reaction-diffusion systems. Under the adiabatic approximation of inhibitor, a two-component reaction-diffusion system is reduced to a one-component reaction-diffusion equation with a convolution term. To find the traveling speed in a reaction-diffusion system with a global coupling term, the stability of the standing pulse and the relation between traveling speed and bifurcation parameter are examined. Additionally, we consider the traveling pulses in the kernel-based Turing model. The stability of the spatially homogeneous state and most unstable wave number are examined. The practical utilities of the convolution representation of reaction-diffusion systems are discussed.
{"title":"Convolution Representation of Traveling Pulses in Reaction-Diffusion Systems","authors":"S. Kawaguchi","doi":"10.1155/2023/1410642","DOIUrl":"https://doi.org/10.1155/2023/1410642","url":null,"abstract":"Convolution representation manifests itself as an important tool in the reduction of partial differential equations. In this study, we consider the convolution representation of traveling pulses in reaction-diffusion systems. Under the adiabatic approximation of inhibitor, a two-component reaction-diffusion system is reduced to a one-component reaction-diffusion equation with a convolution term. To find the traveling speed in a reaction-diffusion system with a global coupling term, the stability of the standing pulse and the relation between traveling speed and bifurcation parameter are examined. Additionally, we consider the traveling pulses in the kernel-based Turing model. The stability of the spatially homogeneous state and most unstable wave number are examined. The practical utilities of the convolution representation of reaction-diffusion systems are discussed.","PeriodicalId":49111,"journal":{"name":"Advances in Mathematical Physics","volume":" ","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48848132","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Based on the wave function expansion method, the dynamic antiplane characteristics of a wedge-shaped quarter-space containing a circular hole are studied in a complex coordinate system. The wedge-shaped medium is decomposed into two subregions along the virtual boundary using the virtual region decomposition method. The scattering wave field in subregion I is constructed by the mirror method, and the standing wave field in region II is constructed by the fractional Bessel function. According to the continuity conditions at the virtual boundary and the stress-free boundary of the circular hole, the unknown coefficients of the wave fields are obtained by the Fourier integral transform, and the analytical solution of the dynamic stress concentration factor (DSCF) of the circular hole is then obtained. Through parametric analysis, the effects of incident wave frequency, geometry of the wedge, and corner slope on the DSCF of the circular hole are discussed. The results show that when the SH-wave is horizontally incidence at high frequencies, the DSCF of the circular hole can be significantly changed by introducing the corner slope. Moreover, when the corner slope is high, the maximum DSCF can be amplified about 1.2 times. Finally, the back propagation (BP) neural network prediction model of DSCF is established, and the coefficient of regression is found to reach more than 0.99.
{"title":"Analysis and Prediction of the Dynamic Antiplane Characteristics of an Elastic Wedge-Shaped Quarter-Space Containing a Circular Hole","authors":"Shenling Liu, Jie Yang, Yue Liu, Q. Liu","doi":"10.1155/2023/9951245","DOIUrl":"https://doi.org/10.1155/2023/9951245","url":null,"abstract":"Based on the wave function expansion method, the dynamic antiplane characteristics of a wedge-shaped quarter-space containing a circular hole are studied in a complex coordinate system. The wedge-shaped medium is decomposed into two subregions along the virtual boundary using the virtual region decomposition method. The scattering wave field in subregion I is constructed by the mirror method, and the standing wave field in region II is constructed by the fractional Bessel function. According to the continuity conditions at the virtual boundary and the stress-free boundary of the circular hole, the unknown coefficients of the wave fields are obtained by the Fourier integral transform, and the analytical solution of the dynamic stress concentration factor (DSCF) of the circular hole is then obtained. Through parametric analysis, the effects of incident wave frequency, geometry of the wedge, and corner slope on the DSCF of the circular hole are discussed. The results show that when the SH-wave is horizontally incidence at high frequencies, the DSCF of the circular hole can be significantly changed by introducing the corner slope. Moreover, when the corner slope is high, the maximum DSCF can be amplified about 1.2 times. Finally, the back propagation (BP) neural network prediction model of DSCF is established, and the coefficient of regression is found to reach more than 0.99.","PeriodicalId":49111,"journal":{"name":"Advances in Mathematical Physics","volume":" ","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43536731","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
M. R. Elahi, Y. Mahmoudi, A. Salimi Shamloo, M. Jahangiri Rad
In this study, the Fredholm hypersingular integral equation of the first kind with a singular right-hand function on the interval − 1 , 1 is solved. The discontinuous solution on the domain − 1 , 1 is approximated by a piecewise polynomial, and a collocation method is introduced to evaluate the unknown coefficients. This method, which can be applied to both linear and nonlinear integral equations, is very simple and straightforward. The presented illustrations relate that the results are very accurate compared to the other methods in the literature.
{"title":"A Novel Collocation Method for Numerical Solution of Hypersingular Integral Equation with Singular Right-Hand Function","authors":"M. R. Elahi, Y. Mahmoudi, A. Salimi Shamloo, M. Jahangiri Rad","doi":"10.1155/2023/5845263","DOIUrl":"https://doi.org/10.1155/2023/5845263","url":null,"abstract":"In this study, the Fredholm hypersingular integral equation of the first kind with a singular right-hand function on the interval \u0000 \u0000 \u0000 \u0000 −\u0000 1\u0000 ,\u0000 1\u0000 \u0000 \u0000 \u0000 is solved. The discontinuous solution on the domain \u0000 \u0000 \u0000 \u0000 −\u0000 1\u0000 ,\u0000 1\u0000 \u0000 \u0000 \u0000 is approximated by a piecewise polynomial, and a collocation method is introduced to evaluate the unknown coefficients. This method, which can be applied to both linear and nonlinear integral equations, is very simple and straightforward. The presented illustrations relate that the results are very accurate compared to the other methods in the literature.","PeriodicalId":49111,"journal":{"name":"Advances in Mathematical Physics","volume":" ","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43425155","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper studies the output regulation problem for a class of switched stochastic systems with sampled-data control. Solutions to the output regulation problem are given in two situations. On the one hand, the exogenous signal is assumed to be a constant. By designing a sampled-data state feedback controller, we obtain that the closed-loop system is mean-square exponentially stable and the regulation output tends to zero. On the other hand, the exogenous signal is assumed to be time-varying with bounded derivative. By constructing a class of Lyapunov-Krasovskii functional and a switching rule which satisfies the average dwell time, sufficient conditions for the solvability of practical output regulation problem are given for switched stochastic systems. Finally, numerical examples are given to illustrate the effectiveness of the method.
{"title":"Output Regulation of Switched Stochastic Systems with Sampled-Data Control","authors":"Xiaoxiao Dong, H. Lan","doi":"10.1155/2023/9549909","DOIUrl":"https://doi.org/10.1155/2023/9549909","url":null,"abstract":"This paper studies the output regulation problem for a class of switched stochastic systems with sampled-data control. Solutions to the output regulation problem are given in two situations. On the one hand, the exogenous signal is assumed to be a constant. By designing a sampled-data state feedback controller, we obtain that the closed-loop system is mean-square exponentially stable and the regulation output tends to zero. On the other hand, the exogenous signal is assumed to be time-varying with bounded derivative. By constructing a class of Lyapunov-Krasovskii functional and a switching rule which satisfies the average dwell time, sufficient conditions for the solvability of practical output regulation problem are given for switched stochastic systems. Finally, numerical examples are given to illustrate the effectiveness of the method.","PeriodicalId":49111,"journal":{"name":"Advances in Mathematical Physics","volume":" ","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47596799","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
G. Akram, Maasoomah Sadaf, M. A. U. Khan, H. Hosseinzadeh
The complex Ginzburg-Landau model appears in the mathematical description of wave propagation in nonlinear optics. In this paper, the fractional complex Ginzburg-Landau model is investigated using the generalized exponential rational function method. The Kerr law and parabolic law are considered to discuss the nonlinearity of the proposed model. The fractional effects are also included using a novel local fractional derivative of order α . Many novel solutions containing trigonometric functions, hyperbolic functions, and exponential functions are acquired using the generalized exponential rational function method. The 3D-surface graphs, 2D-contour graphs, density graphs, and 2D-line graphs of some retrieved solutions are plotted using Maple software. A variety of exact traveling wave solutions are reported including dark, bright, and kink soliton solutions. The nature of the optical solitons is demonstrated through the graphical representations of the acquired solutions for variation in the fractional order of derivative. It is hoped that the acquired solutions will aid in understanding the dynamics of the various physical phenomena and dynamical processes governed by the considered model.
{"title":"Analytical Solutions of the Fractional Complex Ginzburg-Landau Model Using Generalized Exponential Rational Function Method with Two Different Nonlinearities","authors":"G. Akram, Maasoomah Sadaf, M. A. U. Khan, H. Hosseinzadeh","doi":"10.1155/2023/9720612","DOIUrl":"https://doi.org/10.1155/2023/9720612","url":null,"abstract":"The complex Ginzburg-Landau model appears in the mathematical description of wave propagation in nonlinear optics. In this paper, the fractional complex Ginzburg-Landau model is investigated using the generalized exponential rational function method. The Kerr law and parabolic law are considered to discuss the nonlinearity of the proposed model. The fractional effects are also included using a novel local fractional derivative of order \u0000 \u0000 α\u0000 \u0000 . Many novel solutions containing trigonometric functions, hyperbolic functions, and exponential functions are acquired using the generalized exponential rational function method. The 3D-surface graphs, 2D-contour graphs, density graphs, and 2D-line graphs of some retrieved solutions are plotted using Maple software. A variety of exact traveling wave solutions are reported including dark, bright, and kink soliton solutions. The nature of the optical solitons is demonstrated through the graphical representations of the acquired solutions for variation in the fractional order of derivative. It is hoped that the acquired solutions will aid in understanding the dynamics of the various physical phenomena and dynamical processes governed by the considered model.","PeriodicalId":49111,"journal":{"name":"Advances in Mathematical Physics","volume":"1 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64802125","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this note, we establish an integral inequality for compact and orientable real hypersurfaces in complex two-plane Grassmannians , involving the shape operator and the Reeb vector field . Moreover, this integral inequality is optimal in the sense that the real hypersurfaces attaining the equality are completely determined. As direct consequences, some new characterizations of the real hypersurfaces in with isometric Reeb flow can be presented.
{"title":"Some New Characterizations of Real Hypersurfaces with Isometric Reeb Flow in Complex Two-Plane Grassmannians","authors":"Dehe Li, Bo Li, Lifen Zhang","doi":"10.1155/2023/2347915","DOIUrl":"https://doi.org/10.1155/2023/2347915","url":null,"abstract":"<jats:p>In this note, we establish an integral inequality for compact and orientable real hypersurfaces in complex two-plane Grassmannians <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M1\">\u0000 <msub>\u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 </msub>\u0000 <mfenced open=\"(\" close=\")\">\u0000 <mrow>\u0000 <msup>\u0000 <mrow>\u0000 <mi>ℂ</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>m</mi>\u0000 <mo>+</mo>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 </msup>\u0000 </mrow>\u0000 </mfenced>\u0000 </math>\u0000 </jats:inline-formula>, involving the shape operator <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M2\">\u0000 <mi>A</mi>\u0000 </math>\u0000 </jats:inline-formula> and the Reeb vector field <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M3\">\u0000 <mi>ξ</mi>\u0000 </math>\u0000 </jats:inline-formula>. Moreover, this integral inequality is optimal in the sense that the real hypersurfaces attaining the equality are completely determined. As direct consequences, some new characterizations of the real hypersurfaces in <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M4\">\u0000 <msub>\u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 </msub>\u0000 <mfenced open=\"(\" close=\")\">\u0000 <mrow>\u0000 <msup>\u0000 <mrow>\u0000 <mi>ℂ</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>m</mi>\u0000 <mo>+</mo>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 </msup>\u0000 </mrow>\u0000 </mfenced>\u0000 </math>\u0000 </jats:inline-formula> with isometric Reeb flow can be presented.</jats:p>","PeriodicalId":49111,"journal":{"name":"Advances in Mathematical Physics","volume":" ","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47753458","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Due to high rate of electrical device usage of all types and high consumption of electricity, it is necessary to search for alternative way. There are so many models of nature describing many phenomena in energy, magnetic field, heat transfer, and so on. These models are reflected in the delicate nonlinear partial differential equations. The system of coupled Konno-Oono equations is one of those models. We extract some vital solutions for this model, which describe some vital phenomena in applied science. Namely, we applied unified technique in order to perform this mechanism in a completely unified way. Finally, some simulations are performed by utilizing Matlab 18 to exhibit the behaviour of these solutions.
{"title":"Simulating New CKO as a Model of Seismic Sea Waves via Unified Solver","authors":"Hanan A. Alkhidhr, Mahmoud A. E. Abdelrahman","doi":"10.1155/2023/2514899","DOIUrl":"https://doi.org/10.1155/2023/2514899","url":null,"abstract":"Due to high rate of electrical device usage of all types and high consumption of electricity, it is necessary to search for alternative way. There are so many models of nature describing many phenomena in energy, magnetic field, heat transfer, and so on. These models are reflected in the delicate nonlinear partial differential equations. The system of coupled Konno-Oono equations is one of those models. We extract some vital solutions for this model, which describe some vital phenomena in applied science. Namely, we applied unified technique in order to perform this mechanism in a completely unified way. Finally, some simulations are performed by utilizing Matlab 18 to exhibit the behaviour of these solutions.","PeriodicalId":49111,"journal":{"name":"Advances in Mathematical Physics","volume":" ","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45577387","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
S. K. Mohanty, A. N. Dev, S. Sahoo, H. Emadifar, G. Arora
In this investigation, the exact solutions of variable coefficients of generalized Zakharov-Kuznetsov (ZK) equation and the Gardner equation are studied with the help of an extended generalized G ′ / G expansion method. The main objective of this study is to establish the closed-form solutions and dynamics of analytical solutions to the generalized ZK equation and the Gardner equation. The generalized ZK equation and the Gardner equation govern the behavior of nonlinear wave phenomena in the presence of magnetic field in plasma dynamics, turbulence, bottom topography, and quantum field theory. We construct innovative solutions to the models under consideration using various computing tools and a recently developed extended generalized G ′ / G expansion technique. The extended generalized G ′ / G expansion technique is a well-defined and simple technique which is based on the initial assumed solutions of the polynomial of G ′ / G . The derived solutions for both the equations are the hyperbolic, trigonometric, and rational functions. The obtained solutions have shock/kink waves and multisoliton, which depict the dynamical representations of the acquired solutions through the three-dimensional surface plots and the contour plots.
{"title":"Exact Solutions of the Generalized ZK and Gardner Equations by Extended Generalized <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M1\">\u0000 <mfenced open=\"(\" close=\")\">\u0000 <mrow>\u0000 <msup>\u0000 <mrow>\u0000 ","authors":"S. K. Mohanty, A. N. Dev, S. Sahoo, H. Emadifar, G. Arora","doi":"10.1155/2023/3965804","DOIUrl":"https://doi.org/10.1155/2023/3965804","url":null,"abstract":"In this investigation, the exact solutions of variable coefficients of generalized Zakharov-Kuznetsov (ZK) equation and the Gardner equation are studied with the help of an extended generalized \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 G\u0000 \u0000 \u0000 ′\u0000 \u0000 \u0000 /\u0000 G\u0000 \u0000 \u0000 \u0000 expansion method. The main objective of this study is to establish the closed-form solutions and dynamics of analytical solutions to the generalized ZK equation and the Gardner equation. The generalized ZK equation and the Gardner equation govern the behavior of nonlinear wave phenomena in the presence of magnetic field in plasma dynamics, turbulence, bottom topography, and quantum field theory. We construct innovative solutions to the models under consideration using various computing tools and a recently developed extended generalized \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 G\u0000 \u0000 \u0000 ′\u0000 \u0000 \u0000 /\u0000 G\u0000 \u0000 \u0000 \u0000 expansion technique. The extended generalized \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 G\u0000 \u0000 \u0000 ′\u0000 \u0000 \u0000 /\u0000 G\u0000 \u0000 \u0000 \u0000 expansion technique is a well-defined and simple technique which is based on the initial assumed solutions of the polynomial of \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 G\u0000 \u0000 \u0000 ′\u0000 \u0000 \u0000 /\u0000 G\u0000 \u0000 \u0000 \u0000 . The derived solutions for both the equations are the hyperbolic, trigonometric, and rational functions. The obtained solutions have shock/kink waves and multisoliton, which depict the dynamical representations of the acquired solutions through the three-dimensional surface plots and the contour plots.","PeriodicalId":49111,"journal":{"name":"Advances in Mathematical Physics","volume":" ","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-03-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41754388","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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