Pub Date : 2024-10-07DOI: 10.1016/j.cam.2024.116297
Faezeh Aghamohammadi, Fatemeh Shakeri
Tensor, the higher-order data array, naturally arises in many fields, such as information sciences, seismic data reconstruction, physics, video inpainting and so on. In this paper, we intend to provide a new model to recover a tensor, based on self-representation, for the all-mode unfoldings of the desired tensor, regardless of the tensor rank. The suggested idea generalizes self-representation to tensor and recovers an incomplete tensor by reconstructing one fiber by others in such a way that they all belong to the same subspace. We design least-square and low-rank self-representation algorithms based on the Linearized Alternating Direction Method utilizing this concept. We show that the proposed algorithms converge to the rank-minimization of the incomplete tensor.
{"title":"Self representation based methods for tensor completion problem","authors":"Faezeh Aghamohammadi, Fatemeh Shakeri","doi":"10.1016/j.cam.2024.116297","DOIUrl":"10.1016/j.cam.2024.116297","url":null,"abstract":"<div><div>Tensor, the higher-order data array, naturally arises in many fields, such as information sciences, seismic data reconstruction, physics, video inpainting and so on. In this paper, we intend to provide a new model to recover a tensor, based on self-representation, for the all-mode unfoldings of the desired tensor, regardless of the tensor rank. The suggested idea generalizes self-representation to tensor and recovers an incomplete tensor by reconstructing one fiber by others in such a way that they all belong to the same subspace. We design least-square and low-rank self-representation algorithms based on the Linearized Alternating Direction Method utilizing this concept. We show that the proposed algorithms converge to the rank-minimization of the incomplete tensor.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-10-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142445769","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-05DOI: 10.1016/j.cam.2024.116303
Nguyen Van Hung
The purpose of this article is to study new results on the continuity of solution maps for parametric generalized multiobjective games in fuzzy environments. Firstly, we revisit parametric fuzzy generalized multiobjective games. Secondly, we establish some sufficient conditions for upper semi-continuity, Hausdorff upper semi-continuity, closedness and compactness of solution maps for such problem under suitable conditions. Thirdly, we introduce the auxiliary problem of parametric fuzzy generalized multiobjective games and the concept of strong -convexity of objective functions for these problems. Finally, results on the lower semi-continuity, Hausdorff lower semi-continuity, continuity and Hausdorff continuity of solution maps to parametric generalized multiobjective games in fuzzy environments are established and studied. Many examples are given to illustrate our results.
{"title":"On semi-continuity and continuity of solution maps of parametric generalized multiobjective games in fuzzy environments","authors":"Nguyen Van Hung","doi":"10.1016/j.cam.2024.116303","DOIUrl":"10.1016/j.cam.2024.116303","url":null,"abstract":"<div><div>The purpose of this article is to study new results on the continuity of solution maps for parametric generalized multiobjective games in fuzzy environments. Firstly, we revisit parametric fuzzy generalized multiobjective games. Secondly, we establish some sufficient conditions for upper semi-continuity, Hausdorff upper semi-continuity, closedness and compactness of solution maps for such problem under suitable conditions. Thirdly, we introduce the auxiliary problem of parametric fuzzy generalized multiobjective games and the concept of strong <span><math><msub><mrow><mi>K</mi></mrow><mrow><mi>i</mi></mrow></msub></math></span>-convexity of objective functions for these problems. Finally, results on the lower semi-continuity, Hausdorff lower semi-continuity, continuity and Hausdorff continuity of solution maps to parametric generalized multiobjective games in fuzzy environments are established and studied. Many examples are given to illustrate our results.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142426743","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-02DOI: 10.1016/j.cam.2024.116300
Kai Liu , Bin Wang , Ting Fu
Recently, the relaxation technique has been widely used to impose conservation of invariants while retaining the full accuracy of the original method. So far, only a single invariant of a system has been considered. In this work, by a mild generalization of the relaxation technique, the Runge–Kutta–Nyström (RKN) integrators are modified to preserve two invariants for second-order system of Ordinary Differential Equations (ODEs). The proposed integrators can be explicit and of arbitrarily high order. The accuracy of the relaxation RKN integrators and the existence of valid relaxation parameters have been proved. The construction of the new integrators is under the framework of adapted RKN (ARKN) integrators which are specially designed for numerical solving second-order oscillatory systems. Therefore, the proposed integrators could be oscillation-preserving in the sense that they exactly integrate homogeneous oscillatory system . Some numerical experiments are conducted to show the advantage and efficiency of the proposed integrators in comparison with the standard (A)RKN integrators.
{"title":"Relaxation RKN-type integrators that preserve two invariants for second-order (oscillatory) systems","authors":"Kai Liu , Bin Wang , Ting Fu","doi":"10.1016/j.cam.2024.116300","DOIUrl":"10.1016/j.cam.2024.116300","url":null,"abstract":"<div><div>Recently, the relaxation technique has been widely used to impose conservation of invariants while retaining the full accuracy of the original method. So far, only a single invariant of a system has been considered. In this work, by a mild generalization of the relaxation technique, the Runge–Kutta–Nyström (RKN) integrators are modified to preserve two invariants for second-order system of Ordinary Differential Equations (ODEs). The proposed integrators can be explicit and of arbitrarily high order. The accuracy of the relaxation RKN integrators and the existence of valid relaxation parameters have been proved. The construction of the new integrators is under the framework of adapted RKN (ARKN) integrators which are specially designed for numerical solving second-order oscillatory systems. Therefore, the proposed integrators could be oscillation-preserving in the sense that they exactly integrate homogeneous oscillatory system <span><math><mrow><msup><mrow><mi>q</mi></mrow><mrow><mo>′</mo><mo>′</mo></mrow></msup><mo>+</mo><mi>K</mi><mi>q</mi><mo>=</mo><mn>0</mn></mrow></math></span>. Some numerical experiments are conducted to show the advantage and efficiency of the proposed integrators in comparison with the standard (A)RKN integrators.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142426744","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-02DOI: 10.1016/j.cam.2024.116294
E. Aourir , H. Laeli Dastjerdi
The primary goal of this study is to give an approximate algorithm for solving Volterra integro-differential equations (VIDEs) of the third kind using meshless collocation techniques. The basic framework of the novel approach is based on a collocation scheme and radial basis functions (RBFs) created on scattered points. This technique requires no background approximation cells, and the algorithm is powerful, has greater stability, and does not require much computer memory. This approach represents the solution of VIDEs of the third kind by interpolating the RBFs based on the Gauss–Legendre quadrature formula. The problem is reduced to a system of algebraic equations that can be easily solved. A description of the technique for the proposed equations is provided. Furthermore, the error analysis of this scheme is examined. A few numerical experiments are presented to prove the reliability and precision of the suggested approach for solving VIDEs of the third kind. Certain problems were compared with analytical solutions, the moving least squares method, and other methods to prove the effectiveness and applicability of the approach described.
本研究的主要目的是给出一种近似算法，利用无网格配位技术求解第三类 Volterra 积分微分方程 (VIDE)。这种新方法的基本框架基于配位方案和在散点上创建的径向基函数 (RBF)。这种技术不需要背景近似单元，算法功能强大，稳定性更高，而且不需要太多的计算机内存。这种方法通过基于高斯-列根德正交公式的 RBFs 插值来表示第三类 VIDE 的求解。问题被简化为一个代数方程系统，可以轻松求解。本文对拟议方程的技术进行了描述。此外，还研究了该方案的误差分析。为了证明所建议的第三类 VIDE 求解方法的可靠性和精确性，介绍了一些数值实验。将某些问题与分析解法、移动最小二乘法和其他方法进行了比较，以证明所述方法的有效性和适用性。
{"title":"Numerical computational technique for solving Volterra integro-differential equations of the third kind using meshless collocation method","authors":"E. Aourir , H. Laeli Dastjerdi","doi":"10.1016/j.cam.2024.116294","DOIUrl":"10.1016/j.cam.2024.116294","url":null,"abstract":"<div><div>The primary goal of this study is to give an approximate algorithm for solving Volterra integro-differential equations (VIDEs) of the third kind using meshless collocation techniques. The basic framework of the novel approach is based on a collocation scheme and radial basis functions (RBFs) created on scattered points. This technique requires no background approximation cells, and the algorithm is powerful, has greater stability, and does not require much computer memory. This approach represents the solution of VIDEs of the third kind by interpolating the RBFs based on the Gauss–Legendre quadrature formula. The problem is reduced to a system of algebraic equations that can be easily solved. A description of the technique for the proposed equations is provided. Furthermore, the error analysis of this scheme is examined. A few numerical experiments are presented to prove the reliability and precision of the suggested approach for solving VIDEs of the third kind. Certain problems were compared with analytical solutions, the moving least squares method, and other methods to prove the effectiveness and applicability of the approach described.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142426742","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-01DOI: 10.1016/j.cam.2024.116299
Ignace Loris , Simone Rebegoldi
We present a numerical iterative optimization algorithm for the minimization of a cost function consisting of a linear combination of three convex terms, one of which is differentiable, a second one is prox-simple and the third one is the composition of a linear map and a prox-simple function. The algorithm’s special feature lies in its ability to approximate, in a single iteration run, the minimizers of the cost function for many different values of the parameters determining the relative weight of the three terms in the cost function. A proof of convergence of the algorithm, based on an inexact variable metric approach, is also provided. As a special case, one recovers a generalization of the primal–dual algorithm of Chambolle and Pock, and also of the proximal-gradient algorithm. Finally, we show how it is related to a primal–dual iterative algorithm based on inexact proximal evaluations of the non-smooth terms of the cost function.
{"title":"Convergence analysis of a primal–dual optimization-by-continuation algorithm","authors":"Ignace Loris , Simone Rebegoldi","doi":"10.1016/j.cam.2024.116299","DOIUrl":"10.1016/j.cam.2024.116299","url":null,"abstract":"<div><div>We present a numerical iterative optimization algorithm for the minimization of a cost function consisting of a linear combination of three convex terms, one of which is differentiable, a second one is prox-simple and the third one is the composition of a linear map and a prox-simple function. The algorithm’s special feature lies in its ability to approximate, in a single iteration run, the minimizers of the cost function for many different values of the parameters determining the relative weight of the three terms in the cost function. A proof of convergence of the algorithm, based on an inexact variable metric approach, is also provided. As a special case, one recovers a generalization of the primal–dual algorithm of Chambolle and Pock, and also of the proximal-gradient algorithm. Finally, we show how it is related to a primal–dual iterative algorithm based on inexact proximal evaluations of the non-smooth terms of the cost function.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142426768","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-01DOI: 10.1016/j.cam.2024.116295
Lingtao Kong, Chenwei Song
The least squares method is a frequently used technique in fuzzy regression analysis. However, it is highly sensitive to outliers in the dataset. To address this challenge, we propose a novel robust fuzzy regression model based on exponential-type kernel functions. This approach effectively mitigates the influence of poorly fitted observations on the predicted results by reducing their weights. Furthermore, we use the -transformation to guarantee the nonnegativity of the spreads of the predicted response variable. In order to evaluate the performance of our method, a simulation study and three real data sets were considered. The experimental results demonstrate that the proposed method outperforms several popular robust methods in almost all cases. Furthermore, a sensitivity analysis of the estimated parameters provides further evidence of the superior efficiency of the proposed method.
{"title":"Fuzzy robust regression based on exponential-type kernel functions","authors":"Lingtao Kong, Chenwei Song","doi":"10.1016/j.cam.2024.116295","DOIUrl":"10.1016/j.cam.2024.116295","url":null,"abstract":"<div><div>The least squares method is a frequently used technique in fuzzy regression analysis. However, it is highly sensitive to outliers in the dataset. To address this challenge, we propose a novel robust fuzzy regression model based on exponential-type kernel functions. This approach effectively mitigates the influence of poorly fitted observations on the predicted results by reducing their weights. Furthermore, we use the <span><math><mrow><mi>g</mi><mi>h</mi></mrow></math></span>-transformation to guarantee the nonnegativity of the spreads of the predicted response variable. In order to evaluate the performance of our method, a simulation study and three real data sets were considered. The experimental results demonstrate that the proposed method outperforms several popular robust methods in almost all cases. Furthermore, a sensitivity analysis of the estimated parameters provides further evidence of the superior efficiency of the proposed method.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142426740","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-01DOI: 10.1016/j.cam.2024.116301
Francesca Pelosi , Maria Lucia Sampoli , Rida T. Farouki
Although planar Pythagorean–hodograph (PH) curves are compatible with the standard Bernstein–Bézier representations, freely modifying the control points will compromise their PH nature. The present study focuses on identifying control point displacements that ensure a given planar PH curve remains a PH curve. In particular, for planar quintic PH curves , it is shown that finitely-many simultaneous displacements of two control points yield modified quintic PH curves, identified as the solutions of quadratic and cubic equations. As a more practical approach, modification of PH quintics in canonical form with and by the displacement of a single interior control point is considered, with the remaining interior control points being used to minimize a measure of deviation from the original PH quintic. As illustrated by several examples, this approach provides an efficient and intuitive means of effecting reasonable shape modifications within the space of planar quintic PH curves.
{"title":"Control point modifications that preserve the Pythagorean–hodograph nature of planar quintic curves","authors":"Francesca Pelosi , Maria Lucia Sampoli , Rida T. Farouki","doi":"10.1016/j.cam.2024.116301","DOIUrl":"10.1016/j.cam.2024.116301","url":null,"abstract":"<div><div>Although planar Pythagorean–hodograph (PH) curves are compatible with the standard Bernstein–Bézier representations, freely modifying the control points will compromise their PH nature. The present study focuses on identifying control point displacements that ensure a given planar PH curve remains a PH curve. In particular, for planar quintic PH curves <span><math><mrow><mi>r</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow></math></span>, <span><math><mrow><mi>t</mi><mo>∈</mo><mrow><mo>[</mo><mspace></mspace><mn>0</mn><mo>,</mo><mn>1</mn><mspace></mspace><mo>]</mo></mrow></mrow></math></span> it is shown that finitely-many simultaneous displacements of two control points yield modified quintic PH curves, identified as the solutions of quadratic and cubic equations. As a more practical approach, modification of PH quintics in canonical form with <span><math><mrow><mi>r</mi><mrow><mo>(</mo><mn>0</mn><mo>)</mo></mrow><mo>=</mo><mn>0</mn></mrow></math></span> and <span><math><mrow><mi>r</mi><mrow><mo>(</mo><mn>1</mn><mo>)</mo></mrow><mo>=</mo><mn>1</mn></mrow></math></span> by the displacement of a single interior control point is considered, with the remaining interior control points being used to minimize a measure of deviation from the original PH quintic. As illustrated by several examples, this approach provides an efficient and intuitive means of effecting reasonable shape modifications within the space of planar quintic PH curves.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142426741","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-30DOI: 10.1016/j.cam.2024.116290
An Chen , Thai Nguyen , Linyi Qian , Zhixin Yang
In this paper, we study an optimal consumption and asset allocation problem accounting for the fact that individuals’ utility differs across various health states. Our study is based on the assumption that an individual’s health status evolves through a semi-Markov process, where the transition probabilities are contingent on both the present state and the duration spent in that state. The optimal form of stock investment and of consumption is determined analytically. The optimal consumption level is significantly shaped by the integration of health-related factors and can be represented as the inverse of the marginal utility function with respect to time and state price density. Additionally, we introduce a Lagrangian multiplier that can be derived by solving a fixed point problem. While our optimal solutions are applicable to a wide range of utility functions, we provide numerical illustrations specifically using the power utility function in a model encompassing three distinct health states. Transition probabilities are estimated from real data collected by the China Insurance Regulatory Commission (CIRC), using a high-order polynomial Perks formula. We find that the investor’s consumption is higher when health is good, but lower when care is needed.
{"title":"The role of health in consumption and portfolio decision-making: Insights from state-dependent models","authors":"An Chen , Thai Nguyen , Linyi Qian , Zhixin Yang","doi":"10.1016/j.cam.2024.116290","DOIUrl":"10.1016/j.cam.2024.116290","url":null,"abstract":"<div><div>In this paper, we study an optimal consumption and asset allocation problem accounting for the fact that individuals’ utility differs across various health states. Our study is based on the assumption that an individual’s health status evolves through a semi-Markov process, where the transition probabilities are contingent on both the present state and the duration spent in that state. The optimal form of stock investment and of consumption is determined analytically. The optimal consumption level is significantly shaped by the integration of health-related factors and can be represented as the inverse of the marginal utility function with respect to time and state price density. Additionally, we introduce a Lagrangian multiplier that can be derived by solving a fixed point problem. While our optimal solutions are applicable to a wide range of utility functions, we provide numerical illustrations specifically using the power utility function in a model encompassing three distinct health states. Transition probabilities are estimated from real data collected by the China Insurance Regulatory Commission (CIRC), using a high-order polynomial Perks formula. We find that the investor’s consumption is higher when health is good, but lower when care is needed.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142433436","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-28DOI: 10.1016/j.cam.2024.116293
Victor Nawa , Saralees Nadarajah
New estimators for the Fréchet distribution based on the method of logarithmic moments are proposed. These are the first estimators for the Fréchet distribution taking closed forms and applicable for all parameter values. Large sample properties of the proposed estimators are derived. The proposed estimators are compared to the maximum likelihood estimators by simulation.
{"title":"Logarithmic method of moments estimators for the Fréchet distribution","authors":"Victor Nawa , Saralees Nadarajah","doi":"10.1016/j.cam.2024.116293","DOIUrl":"10.1016/j.cam.2024.116293","url":null,"abstract":"<div><div>New estimators for the Fréchet distribution based on the method of logarithmic moments are proposed. These are the first estimators for the Fréchet distribution taking closed forms and applicable for all parameter values. Large sample properties of the proposed estimators are derived. The proposed estimators are compared to the maximum likelihood estimators by simulation.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142358925","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-28DOI: 10.1016/j.cam.2024.116298
Muhammad Amin S. Murad , Faraj M. Omar
In the present paper, the new Kudryashov approach is utilized to construct several novel optical soliton solutions for the generalized integrable (2 + 1)-dimensional nonlinear Schrödinger system with conformable derivative. Additionally, the dynamics of bifurcation behavior and chaos analysis in this system are investigated. We applied bifurcation and chaos theories to enhance our understanding of the planar dynamical system derived from the current model while we obtained and illustrated the chaotic solutions for the perturbed dynamical system using graphs. The study yields a class of new optical soliton solutions, including bell-shaped, wave, dark, dark-bright, dark, multi-dark, and singular soliton solutions. Three-dimensional, two-dimensional, and contour plots are presented to visually demonstrate the physical implications and dynamic characteristics of the current conformable equation system. Further, an analysis is discussed on how the conformable derivative parameter and the parameter of time impact the present optical solutions, demonstrating the system’s importance. It is believed that the solutions analyzed in this study are entirely new and have not been previously reported. These discoveries have the potential to significantly enhance our understanding of nonlinear physical phenomena, especially in nonlinear optics and traffic signaling effects with optical dromion transmission.
{"title":"Optical solitons, dynamics of bifurcation, and chaos in the generalized integrable (2+1)-dimensional nonlinear conformable Schrödinger equations using a new Kudryashov technique","authors":"Muhammad Amin S. Murad , Faraj M. Omar","doi":"10.1016/j.cam.2024.116298","DOIUrl":"10.1016/j.cam.2024.116298","url":null,"abstract":"<div><div>In the present paper, the new Kudryashov approach is utilized to construct several novel optical soliton solutions for the generalized integrable (2 + 1)-dimensional nonlinear Schrödinger system with conformable derivative. Additionally, the dynamics of bifurcation behavior and chaos analysis in this system are investigated. We applied bifurcation and chaos theories to enhance our understanding of the planar dynamical system derived from the current model while we obtained and illustrated the chaotic solutions for the perturbed dynamical system using graphs. The study yields a class of new optical soliton solutions, including bell-shaped, wave, dark, dark-bright, dark, multi-dark, and singular soliton solutions. Three-dimensional, two-dimensional, and contour plots are presented to visually demonstrate the physical implications and dynamic characteristics of the current conformable equation system. Further, an analysis is discussed on how the conformable derivative parameter and the parameter of time impact the present optical solutions, demonstrating the system’s importance. It is believed that the solutions analyzed in this study are entirely new and have not been previously reported. These discoveries have the potential to significantly enhance our understanding of nonlinear physical phenomena, especially in nonlinear optics and traffic signaling effects with optical dromion transmission.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142426739","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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