In this manuscript, we focus on the application of recently developed analytical scheme, namely, the rational sine-Gordon expansion method (SGEM). Some new exact solutions of Riemann wave system and the nonlinear Gross−Pitaevskii equation (GPE) by using this method are extracted. This method is based on the general properties of the SGEM which uses the fundamental properties of trigonometric functions. Many novel analytical solutions such as dark, bright, mixed dark–bright, hyperbolic, and periodic wave solutions are successfully extracted. Physical meanings of solutions are simulated by the various figures in 2D and 3D along with the contour graphs. Strain conditions of the existence are also reported in detail. Finally, modulation instability analysis of the nonlinear GPE is studied in detail.
{"title":"The Modulation Instability Analysis and Analytical Solutions of the Nonlinear Gross−Pitaevskii Model with Conformable Operator and Riemann Wave Equations via Recently Developed Scheme","authors":"Wei Gao, Haci Mehmet Baskonus","doi":"10.1155/2023/4132763","DOIUrl":"https://doi.org/10.1155/2023/4132763","url":null,"abstract":"In this manuscript, we focus on the application of recently developed analytical scheme, namely, the rational sine-Gordon expansion method (SGEM). Some new exact solutions of Riemann wave system and the nonlinear Gross−Pitaevskii equation (GPE) by using this method are extracted. This method is based on the general properties of the SGEM which uses the fundamental properties of trigonometric functions. Many novel analytical solutions such as dark, bright, mixed dark–bright, hyperbolic, and periodic wave solutions are successfully extracted. Physical meanings of solutions are simulated by the various figures in 2D and 3D along with the contour graphs. Strain conditions of the existence are also reported in detail. Finally, modulation instability analysis of the nonlinear GPE is studied in detail.","PeriodicalId":49111,"journal":{"name":"Advances in Mathematical Physics","volume":"16 4","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138508744","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 are concerned with traveling wave solutions for two preys–one predator system with switching effect. First, we discuss that there is no traveling wave solution for this system by using linearization method. Second, applying super-sub solution method we establish the existence of semitraveling wave solutions with the minimal speed explicitly defined. Moreover, using the method of Lyapunov function and LaSalle’s invariance principle, under certain conditions, we obtain that the semitraveling wave solutions connect the only positive equilibrium point at infinity, are actually traveling wave solutions. Finally, the numerical experiments support the validity of our theoretical results.
{"title":"Existence and Nonexistence of Traveling Wave Solutions for a Reaction–Diffusion Preys–Predator System with Switching Effect","authors":"Hang Zhang, Yujuan Jiao, Jinmiao Yang","doi":"10.1155/2023/8942147","DOIUrl":"https://doi.org/10.1155/2023/8942147","url":null,"abstract":"In this paper, we are concerned with traveling wave solutions for two preys–one predator system with switching effect. First, we discuss that there is no traveling wave solution for this system by using linearization method. Second, applying super-sub solution method we establish the existence of semitraveling wave solutions with the minimal speed explicitly defined. Moreover, using the method of Lyapunov function and LaSalle’s invariance principle, under certain conditions, we obtain that the semitraveling wave solutions connect the only positive equilibrium point at infinity, are actually traveling wave solutions. Finally, the numerical experiments support the validity of our theoretical results.","PeriodicalId":49111,"journal":{"name":"Advances in Mathematical Physics","volume":"14 3","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-11-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138508738","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 article, we investigate a nonlinear Petrovsky equation with variable exponent and damping terms. First, we establish the local existence using the Faedo–Galerkin approximation method under the conditions of positive initial energy and appropriate constraints on the variable exponents and . Finally, we prove a finite-time blow-up result for negative initial energy.
{"title":"Well-Posedness and Blow-Up of Solutions for a Variable Exponent Nonlinear Petrovsky Equation","authors":"Nebi Yılmaz, Erhan Pişkin, Ercan Çelik","doi":"10.1155/2023/8866861","DOIUrl":"https://doi.org/10.1155/2023/8866861","url":null,"abstract":"In this article, we investigate a nonlinear Petrovsky equation with variable exponent and damping terms. First, we establish the local existence using the Faedo–Galerkin approximation method under the conditions of positive initial energy and appropriate constraints on the variable exponents <svg height=\"12.7178pt\" style=\"vertical-align:-3.42947pt\" version=\"1.1\" viewbox=\"-0.0498162 -9.28833 19.8424 12.7178\" width=\"19.8424pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,7.71,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,12.208,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,15.172,0)\"></path></g></svg> and <span><svg height=\"12.7178pt\" style=\"vertical-align:-3.42947pt\" version=\"1.1\" viewbox=\"-0.0498162 -9.28833 18.5114 12.7178\" width=\"18.5114pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,6.383,0)\"><use xlink:href=\"#g113-41\"></use></g><g transform=\"matrix(.013,0,0,-0.013,10.881,0)\"><use xlink:href=\"#g113-46\"></use></g><g transform=\"matrix(.013,0,0,-0.013,13.845,0)\"><use xlink:href=\"#g113-42\"></use></g></svg>.</span> Finally, we prove a finite-time blow-up result for negative initial energy.","PeriodicalId":49111,"journal":{"name":"Advances in Mathematical Physics","volume":"17 6","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138508741","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}
The current paper scrutinized the flow dynamics of Eyring–Powell nanofluid on porous stretching cylinder under the effects of magnetic field and viscous dissipation by employing Cattaneo–Christov theory. In order to study impacts of thermophoretic force and Brownian motion, the two-phase (Buongiorno) model is considered. As a consequence, very nonlinear PDEs that govern flow problem were formulated, transformed into ODEs via relevant similarity variables, as well as tackled by utilizing R-K-45 integration scheme along with the shooting technique in the MATLAB R2018a software. Consequently, the numerical simulations reveal that Eyring–Powell fluid, curvature, velocity ratio parameters have the propensity to raise nanofluid velocity. Nanofluid temperature shows an increasing pattern with magnetic, curvature, dissipative heating, and thermophoresis parameters. Besides, Prandtl number, Eyring–Powell fluid, velocity ratio, thermal relaxation time, and porous parameters indicate the declining impact against the nanofluid temperature. Hence, the porous medium reasonably and successfully managed nanofluid temperature as well as the overall thermal system in terms of system cooling. The concentration profile gets fall down with escalating values of Schmidt number, magnetic, curvature, dissipative heating, thermophoresis, Brownian motion, and solutal relaxation time parameters. Moreover, coefficient of the skin friction gets rise for larger values of Eyring–Powell fluid, magnetic and curvature parameters however porous medium and velocity ratio parameters reveal the opposite trends on it. The magnetic, curvature, Eyring–Powell fluid, velocity ratio, and dissipative heating parameters indicate increasing impacts on both Nusselt <svg height="8.8423pt" style="vertical-align:-0.2064009pt" version="1.1" viewbox="-0.0498162 -8.6359 17.9373 8.8423" width="17.9373pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"></path></g><g transform="matrix(.013,0,0,-0.013,10.78,0)"></path></g></svg> and Sherwood <svg height="9.49473pt" style="vertical-align:-0.2063999pt" version="1.1" viewbox="-0.0498162 -9.28833 12.9918 9.49473" width="12.9918pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"></path></g><g transform="matrix(.013,0,0,-0.013,6.136,0)"></path></g></svg> numbers even though both <svg height="8.8423pt" style="vertical-align:-0.2064009pt" version="1.1" viewbox="-0.0498162 -8.6359 17.9373 8.8423" width="17.9373pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><use xlink:href="#g113-79"></use></g><g transform="matrix(.013,0,0,-0.013,10.78,0)"><use xlink:href="#g113-118"></use></g></svg> and <svg height="9.49473pt" style="vertical-align:-0.2063999pt" version="1.1" viewbox="-0.0498162 -9.28833 12.9918 9.49473" width="12.9918pt" xmlns="http://www.w3.
{"title":"Flow Dynamics of Eyring–Powell Nanofluid on Porous Stretching Cylinder under Magnetic Field and Viscous Dissipation Effects","authors":"Ebba Hindebu Rikitu","doi":"10.1155/2023/9996048","DOIUrl":"https://doi.org/10.1155/2023/9996048","url":null,"abstract":"The current paper scrutinized the flow dynamics of Eyring–Powell nanofluid on porous stretching cylinder under the effects of magnetic field and viscous dissipation by employing Cattaneo–Christov theory. In order to study impacts of thermophoretic force and Brownian motion, the two-phase (Buongiorno) model is considered. As a consequence, very nonlinear PDEs that govern flow problem were formulated, transformed into ODEs via relevant similarity variables, as well as tackled by utilizing R-K-45 integration scheme along with the shooting technique in the MATLAB R2018a software. Consequently, the numerical simulations reveal that Eyring–Powell fluid, curvature, velocity ratio parameters have the propensity to raise nanofluid velocity. Nanofluid temperature shows an increasing pattern with magnetic, curvature, dissipative heating, and thermophoresis parameters. Besides, Prandtl number, Eyring–Powell fluid, velocity ratio, thermal relaxation time, and porous parameters indicate the declining impact against the nanofluid temperature. Hence, the porous medium reasonably and successfully managed nanofluid temperature as well as the overall thermal system in terms of system cooling. The concentration profile gets fall down with escalating values of Schmidt number, magnetic, curvature, dissipative heating, thermophoresis, Brownian motion, and solutal relaxation time parameters. Moreover, coefficient of the skin friction gets rise for larger values of Eyring–Powell fluid, magnetic and curvature parameters however porous medium and velocity ratio parameters reveal the opposite trends on it. The magnetic, curvature, Eyring–Powell fluid, velocity ratio, and dissipative heating parameters indicate increasing impacts on both Nusselt <svg height=\"8.8423pt\" style=\"vertical-align:-0.2064009pt\" version=\"1.1\" viewbox=\"-0.0498162 -8.6359 17.9373 8.8423\" width=\"17.9373pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,10.78,0)\"></path></g></svg> and Sherwood <svg height=\"9.49473pt\" style=\"vertical-align:-0.2063999pt\" version=\"1.1\" viewbox=\"-0.0498162 -9.28833 12.9918 9.49473\" width=\"12.9918pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,6.136,0)\"></path></g></svg> numbers even though both <svg height=\"8.8423pt\" style=\"vertical-align:-0.2064009pt\" version=\"1.1\" viewbox=\"-0.0498162 -8.6359 17.9373 8.8423\" width=\"17.9373pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"><use xlink:href=\"#g113-79\"></use></g><g transform=\"matrix(.013,0,0,-0.013,10.78,0)\"><use xlink:href=\"#g113-118\"></use></g></svg> and <svg height=\"9.49473pt\" style=\"vertical-align:-0.2063999pt\" version=\"1.1\" viewbox=\"-0.0498162 -9.28833 12.9918 9.49473\" width=\"12.9918pt\" xmlns=\"http://www.w3.","PeriodicalId":49111,"journal":{"name":"Advances in Mathematical Physics","volume":"46 2","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138508766","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 article is concerned with the initial-value problem of a Schrödinger–Hartree equation in the presence of anisotropic partial/whole harmonic confinement. First, we get a sharp threshold for global existence and finite time blow-up on the ground state mass in the -critical case. Then, some new cross-invariant manifolds and variational problems are constructed to study blow-up versus global well-posedness criterion in the -critical and -supercritical cases. Finally, we research the mass concentration phenomenon of blow-up solutions and the dynamics of the -minimal blow-up solutions in the -critical case. The main ingredients of the proofs are the variational characterisation of the ground state, a suitably refined compactness lemma, and scaling techniques. Our conclusions extend and compensate for some previous results.
{"title":"Sharp Threshold of Global Existence and Mass Concentration for the Schrödinger–Hartree Equation with Anisotropic Harmonic Confinement","authors":"Min Gong, Hui Jian","doi":"10.1155/2023/4316819","DOIUrl":"https://doi.org/10.1155/2023/4316819","url":null,"abstract":"This article is concerned with the initial-value problem of a Schrödinger–Hartree equation in the presence of anisotropic partial/whole harmonic confinement. First, we get a sharp threshold for global existence and finite time blow-up on the ground state mass in the <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M1\"> <msup> <mi>L</mi> <mn>2</mn> </msup> </math> -critical case. Then, some new cross-invariant manifolds and variational problems are constructed to study blow-up versus global well-posedness criterion in the <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M2\"> <msup> <mi>L</mi> <mn>2</mn> </msup> </math> -critical and <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M3\"> <msup> <mi>L</mi> <mn>2</mn> </msup> </math> -supercritical cases. Finally, we research the mass concentration phenomenon of blow-up solutions and the dynamics of the <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M4\"> <msup> <mi>L</mi> <mn>2</mn> </msup> </math> -minimal blow-up solutions in the <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M5\"> <msup> <mi>L</mi> <mn>2</mn> </msup> </math> -critical case. The main ingredients of the proofs are the variational characterisation of the ground state, a suitably refined compactness lemma, and scaling techniques. Our conclusions extend and compensate for some previous results.","PeriodicalId":49111,"journal":{"name":"Advances in Mathematical Physics","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135808863","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 survey some non-blow-up results for the following generalized modified inviscid surface quasigeostrophic equation (GSQG) . This is a generalized surface quasigeostrophic equation (GSQG) with the velocity field related to the scalar by , where . We prove that there is no finite-time singularity if the level set of generalized quasigeostrophic equation does not have a hyperbolic saddle, and the angle of opening of the saddle can go to zero at most as an exponential decay. Moreover, we give some conditions that rule out the formation of sharp fronts for generalized inviscid surface quasigeostrophic equation, and we obtain some estimates on the formation of semiuniform fronts. These results greatly weaken the geometrical assumptions which rule out the collapse of a simple hyperbolic saddle in finite time.
{"title":"Some Conditions of Non-Blow-Up of Generalized Inviscid Surface Quasigeostrophic Equation","authors":"Linrui Li, Mingli Hong, Lin Zheng","doi":"10.1155/2023/4420217","DOIUrl":"https://doi.org/10.1155/2023/4420217","url":null,"abstract":"In this paper, we survey some non-blow-up results for the following generalized modified inviscid surface quasigeostrophic equation (GSQG) <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M1\"> <mfenced open=\"{\" close=\"\"> <mrow> <mtable class=\"smallmatrix\"> <mtr> <mtd columnalign=\"left\"> <msub> <mrow> <mi>θ</mi> </mrow> <mrow> <mi>t</mi> </mrow> </msub> <mo>+</mo> <mi>u</mi> <mo>·</mo> <mo>∇</mo> <mi>θ</mi> <mo>=</mo> <mn>0</mn> <mo>,</mo> </mtd> </mtr> <mtr> <mtd columnalign=\"left\"> <mi>u</mi> <mo>=</mo> <msup> <mrow> <mo>∇</mo> </mrow> <mrow> <mo>⊥</mo> </mrow> </msup> <mi>ψ</mi> <mo>,</mo> </mtd> </mtr> <mtr> <mtd columnalign=\"left\"> <mo>−</mo> <msup> <mrow> <mi>Λ</mi> </mrow> <mrow> <mi>β</mi> </mrow> </msup> <mi>ψ</mi> <mo>=</mo> <mi>θ</mi> <mo>,</mo> </mtd> </mtr> <mtr> <mtd columnalign=\"left\"> <mi>θ</mi> <mfenced open=\"(\" close=\")\"> <mrow> <mi>x</mi> <mo>,</mo> <mn>0</mn> </mrow> </mfenced> <mo>=</mo> <msub> <mrow> <mi>θ</mi> </mrow> <mrow> <mn>0</mn> </mrow> </msub> <mfenced open=\"(\" close=\")\"> <mrow> <mi>x</mi> </mrow> </mfenced> <mo>.</mo> </mtd> </mtr> </mtable> </mrow> </mfenced> </math> . This is a generalized surface quasigeostrophic equation (GSQG) with the velocity field <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M2\"> <mi>u</mi> </math> related to the scalar <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M3\"> <mi>θ</mi> </math> by <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M4\"> <mi>u</mi> <mo>=</mo> <mo>−</mo> <msup> <mrow> <mo>∇</mo> </mrow> <mrow> <mo>⊥</mo> </mrow> </msup> <msup> <mrow> <mi>Λ</mi> </mrow> <mrow> <mo>−</mo> <mi>β</mi> </mrow> </msup> <mi>θ</mi> </math> , where <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M5\"> <mn>1</mn> <mo>≤</mo> <mi>β</mi> <mo>≤</mo> <mn>2</mn> </math> . We prove that there is no finite-time singularity if the level set of generalized quasigeostrophic equation does not have a hyperbolic saddle, and the angle of opening of the saddle can go to zero at most as an exponential decay. Moreover, we give some conditions that rule out the formation of sharp fronts for generalized inviscid surface quasigeostrophic equation, and we obtain some estimates on the formation of semiuniform fronts. These results greatly weaken the geometrical assumptions which rule out the collapse of a simple hyperbolic saddle in finite time.","PeriodicalId":49111,"journal":{"name":"Advances in Mathematical Physics","volume":"386 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136104291","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":"Retracted: The Statistical Analysis of Multidimensional Psychological Characteristics and User Feedback Willingness","authors":"Advances in Mathematical Physics","doi":"10.1155/2023/9837132","DOIUrl":"https://doi.org/10.1155/2023/9837132","url":null,"abstract":"<jats:p />","PeriodicalId":49111,"journal":{"name":"Advances in Mathematical Physics","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135824482","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}
The Darboux transformation (DT) and generalized DT (GDT) have played important roles in constructing multisoliton solutions, rogue wave solutions, and semirational solutions of integrable systems. The main purpose of this article is to extend the DT and GDT to a conformable fractional two-component generalized Hirota (TCGH) equation for revealing novel dynamic characteristics of fractional soliton and semirational solutions. As for the main contributions, specifically, we propose a fractional form of the TCGH equation, provide the associated fractional Lax pair, and obtain fractional soliton and semirational solutions of the fractional TCGH equation by constructing its fractional DT and GDT. In addition, we find that the dominant role of fractional order leads to new dynamic characteristics of the obtained fractional soliton and semirational solutions, mainly including a certain degree of tilt of wave crests and the variations in velocities and wave widths over time during propagation, which are not possessed by the corresponding integer-order TCGH equation. Meanwhile, this study predicts the deceleration propagation of solitons in fractional dimensional media and brings the possibility of exploring the asymmetric regulation mechanism of rogue waves from the perspective of fractional-order dominance.
{"title":"Fractional Soliton and Semirational Solutions of a Fractional Two-Component Generalized Hirota Equation","authors":"Sheng Zhang, Feng Zhu, Bo Xu","doi":"10.1155/2023/9996101","DOIUrl":"https://doi.org/10.1155/2023/9996101","url":null,"abstract":"The Darboux transformation (DT) and generalized DT (GDT) have played important roles in constructing multisoliton solutions, rogue wave solutions, and semirational solutions of integrable systems. The main purpose of this article is to extend the DT and GDT to a conformable fractional two-component generalized Hirota (TCGH) equation for revealing novel dynamic characteristics of fractional soliton and semirational solutions. As for the main contributions, specifically, we propose a fractional form of the TCGH equation, provide the associated fractional Lax pair, and obtain fractional soliton and semirational solutions of the fractional TCGH equation by constructing its fractional DT and GDT. In addition, we find that the dominant role of fractional order leads to new dynamic characteristics of the obtained fractional soliton and semirational solutions, mainly including a certain degree of tilt of wave crests and the variations in velocities and wave widths over time during propagation, which are not possessed by the corresponding integer-order TCGH equation. Meanwhile, this study predicts the deceleration propagation of solitons in fractional dimensional media and brings the possibility of exploring the asymmetric regulation mechanism of rogue waves from the perspective of fractional-order dominance.","PeriodicalId":49111,"journal":{"name":"Advances in Mathematical Physics","volume":"28 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136079757","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 exploration, we reflect on the wave transmission of three-dimensional (3D) nonlinear electron–positron magnetized plasma, counting both hot as well as cold ion. Treated equation acquiesces to nonlinear-modified KdV-Zakharov–Kuznetsov (mKdV-ZK) dynamical 3D form. The model is integrated by the -model expansion scheme and invented few families of ion acoustic solitonic propagation results in term of Jacobi elliptic functions. Various shock waves, bullet like bright soliton, dark soliton, singular soliton, as well as periodic signal solutions, are formed from the Jacobi elliptic solution for different parametric constraints. Some of the solutions are illustrated graphically and analyzed width and height due to change of exist parameters in the solutions. Figures are provided to explain the wave natures and effects of nonlinear and fractional parameters are presented in the same two-dimensional (2D) plots.
{"title":"Ion Acoustic Solitary Wave Solutions to mKdV-ZK Model in Homogeneous Magnetized Plasma","authors":"Mst. Razia Pervin, Harun-Or Roshid, Pinakee Dey, Shewli Shamim Shanta, Sachin Kumar","doi":"10.1155/2023/1901898","DOIUrl":"https://doi.org/10.1155/2023/1901898","url":null,"abstract":"In this exploration, we reflect on the wave transmission of three-dimensional (3D) nonlinear electron–positron magnetized plasma, counting both hot as well as cold ion. Treated equation acquiesces to nonlinear-modified KdV-Zakharov–Kuznetsov (mKdV-ZK) dynamical 3D form. The model is integrated by the <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M1\"> <msup> <mi>φ</mi> <mn>6</mn> </msup> </math> -model expansion scheme and invented few families of ion acoustic solitonic propagation results in term of Jacobi elliptic functions. Various shock waves, bullet like bright soliton, dark soliton, singular soliton, as well as periodic signal solutions, are formed from the Jacobi elliptic solution for different parametric constraints. Some of the solutions are illustrated graphically and analyzed width and height due to change of exist parameters in the solutions. Figures are provided to explain the wave natures and effects of nonlinear and fractional parameters are presented in the same two-dimensional (2D) plots.","PeriodicalId":49111,"journal":{"name":"Advances in Mathematical Physics","volume":"160 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135482243","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}
Hamzeh Zureigat, Mohammad A. Tashtoush, Ali F. Al Jassar, Emad A. Az-Zo’bi, Mohammad W. Alomari
Complex fuzzy sets (CFSs) have recently emerged as a potent tool for expanding the scope of fuzzy sets to encompass wider ranges within the unit disk in the complex plane. This study explores complex fuzzy numbers and introduces their application for the first time in the literature to address a complex fuzzy partial differential equation that involves a complex fuzzy heat equation under Hukuhara differentiability. The researchers utilize an implicit finite difference scheme, namely the Crank–Nicolson method, to tackle complex fuzzy heat equations. The problem’s fuzziness arises from the coefficients in both amplitude and phase terms, as well as in the initial and boundary conditions, with the Convex normalized triangular fuzzy numbers extended to the unit disk in the complex plane. The researchers take advantage of the properties and benefits of CFS theory in the proposed numerical methods and subsequently provide a new proof of the stability under CFS theory. A numerical example is presented to demonstrate the proposed approach’s reliability and feasibility, with the results showing good agreement with the exact solution and relevant theoretical aspects.
{"title":"A Solution of the Complex Fuzzy Heat Equation in Terms of Complex Dirichlet Conditions Using a Modified Crank–Nicolson Method","authors":"Hamzeh Zureigat, Mohammad A. Tashtoush, Ali F. Al Jassar, Emad A. Az-Zo’bi, Mohammad W. Alomari","doi":"10.1155/2023/6505227","DOIUrl":"https://doi.org/10.1155/2023/6505227","url":null,"abstract":"Complex fuzzy sets (CFSs) have recently emerged as a potent tool for expanding the scope of fuzzy sets to encompass wider ranges within the unit disk in the complex plane. This study explores complex fuzzy numbers and introduces their application for the first time in the literature to address a complex fuzzy partial differential equation that involves a complex fuzzy heat equation under Hukuhara differentiability. The researchers utilize an implicit finite difference scheme, namely the Crank–Nicolson method, to tackle complex fuzzy heat equations. The problem’s fuzziness arises from the coefficients in both amplitude and phase terms, as well as in the initial and boundary conditions, with the Convex normalized triangular fuzzy numbers extended to the unit disk in the complex plane. The researchers take advantage of the properties and benefits of CFS theory in the proposed numerical methods and subsequently provide a new proof of the stability under CFS theory. A numerical example is presented to demonstrate the proposed approach’s reliability and feasibility, with the results showing good agreement with the exact solution and relevant theoretical aspects.","PeriodicalId":49111,"journal":{"name":"Advances in Mathematical Physics","volume":"39 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135936894","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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