Pub Date : 2024-05-15DOI: 10.1007/s44198-024-00192-2
Claudio Sierpe, Claudio Vidal
{"title":"Nonlinear Stability of Equilibria in Hamiltonian Systems with Multiple Resonances without Interactions","authors":"Claudio Sierpe, Claudio Vidal","doi":"10.1007/s44198-024-00192-2","DOIUrl":"https://doi.org/10.1007/s44198-024-00192-2","url":null,"abstract":"","PeriodicalId":48904,"journal":{"name":"Journal of Nonlinear Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140972409","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}
Pub Date : 2024-05-13DOI: 10.1007/s44198-024-00195-z
Jicheng Yu, Yuqiang Feng
In this paper, Lie symmetry analysis method is applied to the (2+1)-dimensional time fractional modified Bogoyavlenskii–Schiff equations, which is an important model in physics. The one-dimensional optimal system composed by the obtained Lie symmetries is utilized to reduce the system of (2+1)-dimensional fractional partial differential equations with Riemann–Liouville fractional derivative to the system of (1+1)-dimensional fractional partial differential equations with Erdélyi–Kober fractional derivative. Then the power series method is applied to derive explicit power series solutions for the reduced system. In addition, the new conservation theorem and the generalization of Noether operators are developed to construct the conservation laws for the equations studied.
{"title":"Lie Symmetry Analysis, Power Series Solutions and Conservation Laws of (2+1)-Dimensional Time Fractional Modified Bogoyavlenskii–Schiff Equations","authors":"Jicheng Yu, Yuqiang Feng","doi":"10.1007/s44198-024-00195-z","DOIUrl":"https://doi.org/10.1007/s44198-024-00195-z","url":null,"abstract":"<p>In this paper, Lie symmetry analysis method is applied to the (2+1)-dimensional time fractional modified Bogoyavlenskii–Schiff equations, which is an important model in physics. The one-dimensional optimal system composed by the obtained Lie symmetries is utilized to reduce the system of (2+1)-dimensional fractional partial differential equations with Riemann–Liouville fractional derivative to the system of (1+1)-dimensional fractional partial differential equations with Erdélyi–Kober fractional derivative. Then the power series method is applied to derive explicit power series solutions for the reduced system. In addition, the new conservation theorem and the generalization of Noether operators are developed to construct the conservation laws for the equations studied.</p>","PeriodicalId":48904,"journal":{"name":"Journal of Nonlinear Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140929431","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}
Pub Date : 2024-05-02DOI: 10.1007/s44198-024-00187-z
Vipin Gupta, M. S. Barak, Hijaz Ahmad, Soumik Das, Bandar Almohsen
This research explores the complex interaction between piezoelectric waves and heat-moisture diffusion within a semi-infinite piezoelectric material under hygro-thermal conditions. By employing a two-dimensional Cartesian framework, novel governing equations for a thermo-piezoelectrically orthotropic medium influenced by moisture effects are developed. Accurate representations for key parameters are obtained by utilizing normal mode analysis. The investigation examines the influence of critical factors like moisture content, diffusivity, and temperature diffusivity on the spatial distribution of various physical fields. Additionally, a particular scenario of significance is highlighted. These results have the potential to improve sensor, actuator, and energy-harvesting device performance and dependability.
{"title":"Response of Moisture and Temperature Diffusivity on an Orthotropic Hygro-thermo-piezo-elastic Medium","authors":"Vipin Gupta, M. S. Barak, Hijaz Ahmad, Soumik Das, Bandar Almohsen","doi":"10.1007/s44198-024-00187-z","DOIUrl":"https://doi.org/10.1007/s44198-024-00187-z","url":null,"abstract":"<p>This research explores the complex interaction between piezoelectric waves and heat-moisture diffusion within a semi-infinite piezoelectric material under hygro-thermal conditions. By employing a two-dimensional Cartesian framework, novel governing equations for a thermo-piezoelectrically orthotropic medium influenced by moisture effects are developed. Accurate representations for key parameters are obtained by utilizing normal mode analysis. The investigation examines the influence of critical factors like moisture content, diffusivity, and temperature diffusivity on the spatial distribution of various physical fields. Additionally, a particular scenario of significance is highlighted. These results have the potential to improve sensor, actuator, and energy-harvesting device performance and dependability.</p>","PeriodicalId":48904,"journal":{"name":"Journal of Nonlinear Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140828042","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}
Pub Date : 2024-04-29DOI: 10.1007/s44198-024-00189-x
Mingzhi Mao, Xuyang He
In this paper, we use successive approximations and Picard iterative method to establish the existence and uniqueness of mild solution for a class of doubly perturbed impulsive neutral stochastic functional differential equations with Poisson jumps in Hilbert spaces. An example of a doubly perturbed stochastic differential equation with delays is given to illustrate our main results.
{"title":"Existence of a Class of Doubly Perturbed Stochastic Functional Differential Equations with Poisson Jumps","authors":"Mingzhi Mao, Xuyang He","doi":"10.1007/s44198-024-00189-x","DOIUrl":"https://doi.org/10.1007/s44198-024-00189-x","url":null,"abstract":"<p>In this paper, we use successive approximations and Picard iterative method to establish the existence and uniqueness of mild solution for a class of doubly perturbed impulsive neutral stochastic functional differential equations with Poisson jumps in Hilbert spaces. An example of a doubly perturbed stochastic differential equation with delays is given to illustrate our main results.</p>","PeriodicalId":48904,"journal":{"name":"Journal of Nonlinear Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140810030","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}
Pub Date : 2024-04-29DOI: 10.1007/s44198-024-00190-4
Norah Alshehri, Mohammed Guediri
This paper investigates Ricci solitons on Riemannian hypersurfaces in both Riemannian and Lorentzian manifolds. We provide conditions under which a Riemannian hypersurface, exhibiting specific properties related to a closed conformal vector field of the ambiant manifold, forms a Ricci soliton structure. The characterization involves a delicate balance between geometric quantities and the behavior of the conformal vector field, particularly its tangential component. We extend the analysis to ambient manifolds with constant sectional curvature and establish that, under a simple condition, the hypersurface becomes totally umbilical, implying constant mean curvature and sectional curvature. For compact hypersurfaces, we further characterize the nature of the Ricci soliton.
{"title":"Ricci Solitons on Riemannian Hypersurfaces Arising from Closed Conformal Vector Fields in Riemannian and Lorentzian Manifolds","authors":"Norah Alshehri, Mohammed Guediri","doi":"10.1007/s44198-024-00190-4","DOIUrl":"https://doi.org/10.1007/s44198-024-00190-4","url":null,"abstract":"<p>This paper investigates Ricci solitons on Riemannian hypersurfaces in both Riemannian and Lorentzian manifolds. We provide conditions under which a Riemannian hypersurface, exhibiting specific properties related to a closed conformal vector field of the ambiant manifold, forms a Ricci soliton structure. The characterization involves a delicate balance between geometric quantities and the behavior of the conformal vector field, particularly its tangential component. We extend the analysis to ambient manifolds with constant sectional curvature and establish that, under a simple condition, the hypersurface becomes totally umbilical, implying constant mean curvature and sectional curvature. For compact hypersurfaces, we further characterize the nature of the Ricci soliton.</p>","PeriodicalId":48904,"journal":{"name":"Journal of Nonlinear Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140809891","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}
Pub Date : 2024-04-25DOI: 10.1007/s44198-024-00175-3
A. Sakabekov, Y. Auzhani, Ryskul Yergazina, Saltanat Madaliyeva
{"title":"Determination of the Speed and Surface Temperature of Aircraft Using the Second Approximation of the System of Moment Equations","authors":"A. Sakabekov, Y. Auzhani, Ryskul Yergazina, Saltanat Madaliyeva","doi":"10.1007/s44198-024-00175-3","DOIUrl":"https://doi.org/10.1007/s44198-024-00175-3","url":null,"abstract":"","PeriodicalId":48904,"journal":{"name":"Journal of Nonlinear Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140655769","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}
Accurate inversion of atmospheric turbulence strength is a challenging problem in modern turbulence research due to its practical significance. Inspired by transfer learning, we propose a new neural network method consisting of convolution and pooling modules for the atmospheric turbulence strength inversion problem. Its input is the intensity image of the beam and its output is the refractive index structure constant characterizing the atmospheric turbulence strength. We evaluate the inversion performance of the neural network at different beams. Meanwhile, to enhance the generalisation of the network, we mix data sets from different turbulence environments to construct new data sets. Additionally, the inverted atmospheric turbulence strength is used as a priori information to help identify turbulent targets. Experimental results demonstrate the effectiveness of our proposed method.
{"title":"A Neural Network Method for Inversion of Turbulence Strength","authors":"Weishi Yin, Baoyin Zhang, Pinchao Meng, Linhua Zhou, Dequan Qi","doi":"10.1007/s44198-024-00186-0","DOIUrl":"https://doi.org/10.1007/s44198-024-00186-0","url":null,"abstract":"<p>Accurate inversion of atmospheric turbulence strength is a challenging problem in modern turbulence research due to its practical significance. Inspired by transfer learning, we propose a new neural network method consisting of convolution and pooling modules for the atmospheric turbulence strength inversion problem. Its input is the intensity image of the beam and its output is the refractive index structure constant characterizing the atmospheric turbulence strength. We evaluate the inversion performance of the neural network at different beams. Meanwhile, to enhance the generalisation of the network, we mix data sets from different turbulence environments to construct new data sets. Additionally, the inverted atmospheric turbulence strength is used as a priori information to help identify turbulent targets. Experimental results demonstrate the effectiveness of our proposed method.</p>","PeriodicalId":48904,"journal":{"name":"Journal of Nonlinear Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140561204","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}
Pub Date : 2024-04-03DOI: 10.1007/s44198-024-00181-5
Abstract
In this paper, we introduce a curvilinear coordinate transformation to study the bifurcation of periodic solutions from a 2-degree-of-freedom Hamiltonian system, when it is perturbed in ({textbf{R}}^{m+4}), where m represents any positive integer. The extended Melnikov function is obtained by constructing a Poincaré map on the curvilinear coordinate frame of the trajectory of the unperturbed system. Then the criteria for bifurcation of periodic solutions of these Hamiltonian systems under isochronous and non-isochronous conditions are obtained. As for its application, we study the number of periodic solutions of a composite piezoelectric cantilever rectangular plate system whose averaged equation can be transformed into a ((2+4))-dimensional dynamical system. Furthermore, under the two resonance conditions of 1:1 and 1:2, we obtain the periodic solution numbers of this system with the variation of parametric excitation coefficient (p_1.)
{"title":"Bifurcation of Multiple Periodic Solutions for a Class of Nonlinear Dynamical Systems in $$(m+4)$$ -Dimension","authors":"","doi":"10.1007/s44198-024-00181-5","DOIUrl":"https://doi.org/10.1007/s44198-024-00181-5","url":null,"abstract":"<h3>Abstract</h3> <p>In this paper, we introduce a curvilinear coordinate transformation to study the bifurcation of periodic solutions from a 2-degree-of-freedom Hamiltonian system, when it is perturbed in <span> <span>({textbf{R}}^{m+4})</span> </span>, where <em>m</em> represents any positive integer. The extended Melnikov function is obtained by constructing a Poincaré map on the curvilinear coordinate frame of the trajectory of the unperturbed system. Then the criteria for bifurcation of periodic solutions of these Hamiltonian systems under isochronous and non-isochronous conditions are obtained. As for its application, we study the number of periodic solutions of a composite piezoelectric cantilever rectangular plate system whose averaged equation can be transformed into a <span> <span>((2+4))</span> </span>-dimensional dynamical system. Furthermore, under the two resonance conditions of 1:1 and 1:2, we obtain the periodic solution numbers of this system with the variation of parametric excitation coefficient <span> <span>(p_1.)</span> </span></p>","PeriodicalId":48904,"journal":{"name":"Journal of Nonlinear Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140561068","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}
Pub Date : 2024-04-02DOI: 10.1007/s44198-024-00184-2
Abstract
In this paper, we consider the nonlinear Schrödinger’s equation with Kudryashov’s law of refractive index. By using the method of dynamical systems, we obtain bifurcations of the phase portraits of the traveling wave system under different parameter conditions. Corresponding to some special level curves, we derive possible exact explicit parametric representations of solutions (including peakon, periodic peakon, solitary wave solutions and compactons) under different parameter conditions.
{"title":"Peakon, Periodic Peakons, Compactons and Bifurcations of nonlinear Schrödinger’s Equation with Kudryashov’s Law of Refractive Index","authors":"","doi":"10.1007/s44198-024-00184-2","DOIUrl":"https://doi.org/10.1007/s44198-024-00184-2","url":null,"abstract":"<h3>Abstract</h3> <p>In this paper, we consider the nonlinear Schrödinger’s equation with Kudryashov’s law of refractive index. By using the method of dynamical systems, we obtain bifurcations of the phase portraits of the traveling wave system under different parameter conditions. Corresponding to some special level curves, we derive possible exact explicit parametric representations of solutions (including peakon, periodic peakon, solitary wave solutions and compactons) under different parameter conditions.</p>","PeriodicalId":48904,"journal":{"name":"Journal of Nonlinear Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140561203","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}