Advances in Mathematical Physics最新文献

{"title":"Interaction Solutions of the (2+1)-Dimensional Sawada-Kotera Equation","authors":"Yong Meng","doi":"10.1155/2023/9472715","DOIUrl":"https://doi.org/10.1155/2023/9472715","url":null,"abstract":"The N-soliton solution of the (2+1)-dimensional Sawada-Kotera equation is given by using the Hirota bilinear method, and then, the conjugate parameter method and the long-wave limit method are used to get the breather solution and the lump solution, as well as the interaction solution of the elastic collision properties between them. In addition, according to the expression of the lump-type soliton solution and the striped soliton solution, the completely inelastic collision, rebound, absorption, splitting, and other particle characteristics of the two solitons in the interaction process are directly studied with the simulation method, which reveals the laws of physics reflected behind the phenomenon.","PeriodicalId":49111,"journal":{"name":"Advances in Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2023-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44428399","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}

{"title":"Dynamical Property of the Shift Map under Group Action","authors":"Zhan-Huai Ji","doi":"10.1155/2022/5969042","DOIUrl":"https://doi.org/10.1155/2022/5969042","url":null,"abstract":"<jats:p>Firstly, we introduced the concept of <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M1\">\u0000 <mi>G</mi>\u0000 <mo>‐</mo>\u0000 </math>\u0000 </jats:inline-formula>Lipschitz tracking property, <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M2\">\u0000 <mi>G</mi>\u0000 <mo>‐</mo>\u0000 </math>\u0000 </jats:inline-formula>asymptotic average tracking property, and <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M3\">\u0000 <mi>G</mi>\u0000 <mo>‐</mo>\u0000 </math>\u0000 </jats:inline-formula>periodic tracking property. Secondly, we studied their dynamical properties and topological structure and obtained the following conclusions: (1) let <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M4\">\u0000 <mfenced open=\"(\" close=\")\">\u0000 <mrow>\u0000 <mi>X</mi>\u0000 <mo>,</mo>\u0000 <mi>d</mi>\u0000 </mrow>\u0000 </mfenced>\u0000 </math>\u0000 </jats:inline-formula> be compact metric <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M5\">\u0000 <mi>G</mi>\u0000 <mo>‐</mo>\u0000 </math>\u0000 </jats:inline-formula>space and the metric <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M6\">\u0000 <mi>d</mi>\u0000 </math>\u0000 </jats:inline-formula> be invariant to <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M7\">\u0000 <mi>G</mi>\u0000 </math>\u0000 </jats:inline-formula>. Then, <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M8\">\u0000 <mi>σ</mi>\u0000 </math>\u0000 </jats:inline-formula> has <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M9\">\u0000 <mover accent=\"true\">\u0000 <mi>G</mi>\u0000 <mo stretchy=\"true\">¯</mo>\u0000 </mover>\u0000 <mo>‐</mo>\u0000 </math>\u0000 </jats:inline-formula>asymptotic average tracking property; (2) let <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M10\">\u0000 <mfenced open=\"(\" close=\")\">\u0000 <mrow>\u0000 ","PeriodicalId":49111,"journal":{"name":"Advances in Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2022-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43525305","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}

{"title":"Wave Breaking and Global Existence for the Generalized Periodic Camassa-Holm Equation with the Weak Dissipation","authors":"Ying Zhang, Congming Peng","doi":"10.1155/2022/6955014","DOIUrl":"https://doi.org/10.1155/2022/6955014","url":null,"abstract":"In this paper, a family of the weakly dissipative periodic Camassa-Holm type equation cubic and quartic nonlinearities is considered. The precise blow-up scenarios of strong solutions and several conditions on the initial data to guarantee blow-up of the induced solutions are described in detail. Finally, we establish a sufficient condition for global solutions.","PeriodicalId":49111,"journal":{"name":"Advances in Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2022-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46268928","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}

{"title":"Optical Wave Phenomena in Birefringent Fibers Described by Space-Time Fractional Cubic-Quartic Nonlinear Schrödinger Equation with the Sense of Beta and Conformable Derivative","authors":"M. F. Uddin, M. Hafez","doi":"10.1155/2022/7265164","DOIUrl":"https://doi.org/10.1155/2022/7265164","url":null,"abstract":"The work explores the optical wave solutions along with their graphical representations by proposing the coupled spatial-temporal fractional cubic-quartic nonlinear Schrödinger equation with the sense of two fractal derivatives (beta and conformable derivative) and Kerr law nonlinearity for birefringent fibers. The new extended direct algebraic method for the first time is implemented to achieve this goal. Many optical solutions are listed along with their existence criteria. Based on the existence criteria, the cubic-quartic bright, and singular optical soliton, periodic pulse, and rouge wave profiles are supported in birefringent fibers with the influence of both beta and conformable derivative parameter.","PeriodicalId":49111,"journal":{"name":"Advances in Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2022-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47646842","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}

{"title":"Two-Dimensional Fredholm Integro-Differential Equation with Singular Kernel and Its Numerical Solutions","authors":"A. M. Al-Bugami","doi":"10.1155/2022/2501947","DOIUrl":"https://doi.org/10.1155/2022/2501947","url":null,"abstract":"In this paper, we introduce the nonlinear Fredholm integro-differential equation of the second kind with singular kernel in two-dimensional NT-DFIDE. Furthermore, we study this new equation numerically. The existence of a unique solution of the equation is proved. The numerical results of NT-DFIDE are obtained by the following methods: Toeplitz matrix method (TMM) and product Nystrom method (PNM). The given applications showed the efficiency of these methods.","PeriodicalId":49111,"journal":{"name":"Advances in Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2022-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43768180","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}

{"title":"Abundant Exact Soliton Solutions of the (\u0000 2\u0000 +\u0000 1\u0000 )-Dimensional Heisenberg Ferromagnetic Spin Chain Equation Based on the Jacobi Elliptic Function Ideas","authors":"Qinghao Zhu, Jian-ming Qi","doi":"10.1155/2022/7422491","DOIUrl":"https://doi.org/10.1155/2022/7422491","url":null,"abstract":"The Heisenberg ferromagnetic spin chain equation (HFSCE) is very important in modern magnetism theory. HFSCE expounded the nonlinear long-range ferromagnetic ordering magnetism. Also, it depicts the characteristic of magnetism to many insulating crystals as well as interaction spins. Moreover, the ferromagnetism plays a fundamental role in modern technology and industry and it is principal for many electrical and electromechanical devices such as generators, electric motors, and electromagnets. In this article, the exact solutions of the nonlinear (\u0000 \u0000 2\u0000 +\u0000 1\u0000 \u0000 )-dimensional HFSCE are successfully examined by an extended modified version of the Jacobi elliptic expansion method (EMVJEEM). Consequently, much more new Jacobi elliptic traveling wave solutions are found. These new solutions have not yet been reported in the studied models. For the study models, the new solutions are singular solitons not yet observed. Additionally, certain interesting 3D and 2D figures are performed on the obtained solutions. The geometrical representation of the HFSCE provides the dynamical information to explain the physical phenomena. The results will be significant to understand and study the (\u0000 \u0000 2\u0000 +\u0000 1\u0000 \u0000 )-dimensional HFSCE. Therefore, further studying EMVJEEM may help researchers to seek for more soliton solutions to other nonlinear differential equations.","PeriodicalId":49111,"journal":{"name":"Advances in Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2022-12-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48538656","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}

{"title":"Some Exact Solutions to Generalized Kadomtsev-Petviashvili Equation","authors":"Bao Wang, Zhiqiang Chen","doi":"10.1155/2022/9882817","DOIUrl":"https://doi.org/10.1155/2022/9882817","url":null,"abstract":"Most of the papers have explored the interactions between solitons with a zero background, while reports about exact solutions for nonzero background are rare. Hence, this paper is aimed at exploring the breather, lump, and interaction solutions with a small perturbation to (\u0000 \u0000 2\u0000 +\u0000 1\u0000 \u0000 )-dimensional generalized Kadomtsev-Petviashvili (gKP) equation. General high-order periodic breather solutions are obtained using Hirota’s bilinear method with a small perturbation. At the same time, combining the use of long wave limit methods and module resonance constraints, general lump solutions and mixed solutions to gKP equation are generated. Finally, the space-time structures of the breather solutions, lump solutions, and interaction solutions are investigated and discussed.","PeriodicalId":49111,"journal":{"name":"Advances in Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2022-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46750702","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}

{"title":"Coupled Fixed Point Theorem for the Generalized Langevin Equation with Four-Point and Strip Conditions","authors":"A. Salem, Noorah Mshary","doi":"10.1155/2022/1724221","DOIUrl":"https://doi.org/10.1155/2022/1724221","url":null,"abstract":"By considering a metric space with partially ordered sets, we employ the coupled fixed point type to scrutinize the uniqueness theory for the Langevin equation that included two generalized orders. We analyze our problem with four-point and strip conditions. The description of the rigid plate bounded by a Newtonian fluid is provided as an application of our results. The exact solution of this problem and approximate solutions are compared.","PeriodicalId":49111,"journal":{"name":"Advances in Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2022-11-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47068482","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}

{"title":"A Well-Behaved Anisotropic Strange Star Model","authors":"Amos V. Mathias, J. Sunzu","doi":"10.1155/2022/7243750","DOIUrl":"https://doi.org/10.1155/2022/7243750","url":null,"abstract":"We obtain a new nonsingular exact model for compact stellar objects by using the Einstein field equations. The model is consistent with stellar star with anisotropic quark matter in the absence of electric field. Our treatment considers spacetime geometry which is static and spherically symmetric. Ansatz of a rational form of one of the gravitational potentials is made to generate physically admissible results. The balance of gravitational, hydrostatic, and anisotropic forces within the stellar star is tested by analysing the Tolman-Oppenheimer-Volkoff (TOV) equation. Several stellar objects with masses and radii comparable with observations found in the past are generated. Our model obeys different stability tests and energy conditions. The profiles for the potentials, matter variables, stability, and energy conditions are well behaved.","PeriodicalId":49111,"journal":{"name":"Advances in Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2022-11-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44392984","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}

{"title":"A Bayesian-Weighted Inverse Gaussian Regression Model with Application to Seismological Data","authors":"Ehsan Mesdaghi, A. Fallah, R. Farnoosh, G. Yari","doi":"10.1155/2022/3943930","DOIUrl":"https://doi.org/10.1155/2022/3943930","url":null,"abstract":"Developing an efficient model for analyzing right-skewed positive observations has a long history, and many authors have attempt in this direction. This is because the common analytic modeling procedures such as linear regression are often inappropriate for such data and leads to inadequate results. In this article, we proposed a new model for regression analysis of the right-skewed data by assuming the weighted inverse Gaussian, as a great flexible distribution, for response observations. In the proposed model, the complementary reciprocal of the location parameter of response variable is considered to be a linear function of the explanatory variables. We developed a fully Bayesian framework to infer about the model parameters based on a general noninformative prior structure and employed a Gibbs sampler to derive the posterior inferences by using the Markov chain Monte Carlo methods. A comparative simulation study is worked out to assess and compare the proposed model with other usual competitor models, and it is observed that efficiency is quite satisfactory. A real seismological data set is also analyzed to explain the applicability of the proposed Bayesian model and to access its performance. The results indicate to the more accuracy of proposed regression model in estimation of model parameters and prediction of future observations in comparison to its usual competitors in literature. Particularly, the relative prediction efficiency of the proposed regression model to the inverse Gaussian and log-normal regression models has been obtained to be 1.16 and 64, respectively, for the real-world example discussed in this paper.","PeriodicalId":49111,"journal":{"name":"Advances in Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2022-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64776875","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}