Communications in Analysis and Mechanics最新文献_第2页

Conservation laws analysis of nonlinear partial differential equations and their linear soliton solutions and Hamiltonian structures 非线性偏微分方程及其线性孤子解和哈密顿结构的守恒律分析

Communications in Analysis and Mechanics Pub Date : 1900-01-01 DOI: 10.3934/cam.2023002

Long Ju, Jian Zhou, Yufeng Zhang

{"title":"Conservation laws analysis of nonlinear partial differential equations and their linear soliton solutions and Hamiltonian structures","authors":"Long Ju, Jian Zhou, Yufeng Zhang","doi":"10.3934/cam.2023002","DOIUrl":"https://doi.org/10.3934/cam.2023002","url":null,"abstract":"This article mainly uses two methods of solving the conservation laws of two partial differential equations and a system of equations. The first method is to construct the conservation law directly and the second method is to apply the Ibragimov method to solve the conservation laws of the target equation systems, which are constructed based on the symmetric rows of the target equation system. In this paper, we select two equations and an equation system, and we try to apply these two methods to the combined KdV-MKdV equation, the Klein-Gordon equation and the generalized coupled KdV equation, and simply verify them. The combined KdV-MKdV equation describes the wave propagation of bound particles, sound waves and thermal pulses. The Klein-Gordon equation describes the nonlinear sine-KG equation that simulates the motion of the Josephson junction, the rigid pendulum connected to the stretched wire, and the dislocations in the crystal. And the coupled KdV equation has also attracted a lot of research due to its importance in theoretical physics and many scientific applications. In the last part of the article, we try to briefly analyze the Hamiltonian structures and adjoint symmetries of the target equations, and calculate their linear soliton solutions.","PeriodicalId":233941,"journal":{"name":"Communications in Analysis and Mechanics","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131768991","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 3

Lie symmetry analysis, particular solutions and conservation laws for the dissipative (2 + 1)- dimensional AKNS equation 耗散(2 + 1)维AKNS方程的李对称分析、特解和守恒定律

Communications in Analysis and Mechanics Pub Date : 1900-01-01 DOI: 10.3934/cam.2023024

Sixing Tao

{"title":"Lie symmetry analysis, particular solutions and conservation laws for the dissipative (2 + 1)- dimensional AKNS equation","authors":"Sixing Tao","doi":"10.3934/cam.2023024","DOIUrl":"https://doi.org/10.3934/cam.2023024","url":null,"abstract":"The dissipative (2 + 1)-dimensional AKNS equation is considered in this paper. First, the Lie symmetry analysis method is applied to the dissipative (2 + 1)-dimensional AKNS and six point symmetries are obtained. Symmetry reductions are performed by utilizing these obtained point symmetries and four differential equations are derived, including a fourth-order ordinary differential equation and three partial differential equations. Thereafter, the direct integration approach and the $ (G'/G^{2})- $expansion method are employed to solve the ordinary differential respectively. As a result, a periodic solution in terms of the Weierstrass elliptic function is obtained via the the direct integration approach, while six kinds of including the hyperbolic function types and the hyperbolic function types are derived via the $ (G'/G^{2})- $expansion method. The corresponding graphical representation of the obtained solutions are presented by choosing suitable parametric values. Finally, the multiplier technique and the classical Noether's theorem are employed to derive conserved vectors for the dissipative (2 + 1)-dimensional AKNS respectively. Consequently, eight local conservation laws for the dissipative (2 + 1)-dimensional AKNS equation are presented by utilizing the multiplier technique and five local conservation laws are derived by invoking Noether's theorem.","PeriodicalId":233941,"journal":{"name":"Communications in Analysis and Mechanics","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115995442","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

A short proof of cuplength estimates on Lagrangian intersections 拉格朗日交点上偶距估计的一个简短证明

Communications in Analysis and Mechanics Pub Date : 1900-01-01 DOI: 10.3934/cam.2023003

Wenmin Gong

引用次数: 1

Analysis of small oscillations of a pendulum partially filled with a viscoelastic fluid 部分充满粘弹性流体的摆的小振荡分析

Communications in Analysis and Mechanics Pub Date : 1900-01-01 DOI: 10.3934/cam.2023019

H. Essaouini, P. Capodanno

引用次数: 0

Laguerre BV spaces, Laguerre perimeter and their applications 拉盖尔BV空间，拉盖尔周长及其应用

Communications in Analysis and Mechanics Pub Date : 1900-01-01 DOI: 10.3934/cam.2023011

Heming Wang, Yu Liu

引用次数: 0

On criticality coupled sub-Laplacian systems with Hardy type potentials on Stratified Lie groups 分层李群上具有Hardy型势的临界耦合子拉普拉斯系统

Communications in Analysis and Mechanics Pub Date : 1900-01-01 DOI: 10.3934/cam.2023005

Jinguo Zhang, Shuhai Zhu

{"title":"On criticality coupled sub-Laplacian systems with Hardy type potentials on Stratified Lie groups","authors":"Jinguo Zhang, Shuhai Zhu","doi":"10.3934/cam.2023005","DOIUrl":"https://doi.org/10.3934/cam.2023005","url":null,"abstract":"In this work, our main concern is to study the existence and multiplicity of solutions for the following sub-elliptic system with Hardy type potentials and multiple critical exponents on Carnot group\u0000\u0000 begin{document}$ begin{equation*} left{begin{aligned} &-Delta_{mathbb{G}}u = frac{psi^{alpha}|u|^{2^*(alpha)-2}u}{d(z)^{alpha}}+ frac{p_{1}}{2^*(gamma)}frac{psi^{gamma}|u|^{p_{1}-2}u|v|^{p_{2}}}{d(z, z_{0})^{gamma}} +lambda h(z)frac{psi^{sigma}|u|^{q-2}u}{d(z)^{sigma}} , , & text{in } , , Omega, &-Delta_{mathbb{G}}v = frac{psi^{beta}|v|^{2^*(beta)-2}v}{d(z)^{beta}}+ frac{p_{2}}{2^*(gamma)}frac{psi^{gamma}|u|^{p_{1}}|v|^{p_{2}-2}v}{d(z, z_{0})^{gamma}} +lambda h(z)frac{psi^{sigma}|v|^{q-2}v}{d(z)^{sigma}}, , &text{in } , , Omega, &quad u = v = 0, , &text{on } , , partialOmega, end{aligned}right. end{equation*} $end{document} \u0000where $ -Delta_{mathbb{G}} $ is a sub-Laplacian on Carnot group $ mathbb{G} $, $ alpha, beta, gamma, sigmain [0, 2) $, $ d $ is the $ Delta_{mathbb{G}} $-natural gauge, $ psi = |nabla_{mathbb{G}}d| $ and $ nabla_{mathbb{G}} $ is the horizontal gradient associated to $ Delta_{mathbb{G}} $. The positive parameters $ lambda $, $ q $ satisfy $ 0 < lambda < infty $, $ 1 < q < 2 $, and $ p_{1} $, $ p_{2} > 1 $ with $ p_{1}+p_{2} = 2^*(gamma) $, here $ 2^*(alpha): = frac{2(Q-alpha)}{Q-2} $, $ 2^*(beta): = frac{2(Q-beta)}{Q-2} $ and $ 2^*(gamma) = frac{2(Q-gamma)}{Q-2} $ are the critical Hardy-Sobolev exponents, $ Q $ is the homogeneous dimension of the space $ mathbb{G} $. By means of variational methods and the mountain-pass theorem of Ambrosetti and Rabonowitz, we study the existence of multiple solutions to the sub-elliptic system.","PeriodicalId":233941,"journal":{"name":"Communications in Analysis and Mechanics","volume":"188 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121527746","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Conformal-type energy estimates on hyperboloids and the wave-Klein-Gordon model of self-gravitating massive fields 双曲面的共形能量估计和自引力场的波-克莱因-戈登模型

Communications in Analysis and Mechanics Pub Date : 1900-01-01 DOI: 10.3934/cam.2023007

Senhao Duan, Yue Ma, Weidong Zhang

引用次数: 0

Global attractors for a nonlinear plate equation modeling the oscillations of suspension bridges 悬索桥振动非线性板方程的全局吸引子

Communications in Analysis and Mechanics Pub Date : 1900-01-01 DOI: 10.3934/cam.2023021

Yang Liu

引用次数: 0

A possible interpretation of financial markets affected by dark volatility 金融市场受黑暗波动影响的一种可能解释

Communications in Analysis and Mechanics Pub Date : 1900-01-01 DOI: 10.3934/cam.2023006

R. Pinčák, A. Pigazzini, Saeid Jafari, Özge Korkmaz, C. Özel, E. Bartoš

引用次数: 0

Solutions for a class of problems driven by an anisotropic $ (p, q) $-Laplacian type operator 一类由各向异性$ (p, q) $-拉普拉斯算子驱动的问题的解

Communications in Analysis and Mechanics Pub Date : 1900-01-01 DOI: 10.3934/cam.2023026

Leandro Tavares

引用次数: 0