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Computer assisted proof of branches of stationary and periodic solutions, and Hopf bifurcations, for dissipative PDEs [PDF]
Communications in Nonlinear Science and Numerical Simulation, 2022 We discuss an approach to the computer assisted proof of the existence of branches of stationary and periodic solutions for dissipative PDEs, using the Brussellator system with diffusion and Dirichlet boundary conditions as an example, We also consider the case where the branch of periodic solutions emanates from a branch of stationary solutions ...
Gianni Arioli
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Families of Periodic Solutions for Some Hamiltonian PDEs [PDF]
SIAM Journal on Applied Dynamical Systems, 2017 This work studies time-periodic solutions for two Hamiltonian PDE's on a finite interval \([0,\pi]\): the nonlinear wave equation \(u_{tt}-u_{xx}=\pm u^3\), with Dirichlet boundary conditions, and the nonlinear beam equation \(u_{tt}+u_{xxxx}=\pm u^3\) on a finite interval with Navier boundary conditions (the function and its second derivative vanishes
Gianni Arioli, Hans Koch
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Communications in Nonlinear Science and Numerical Simulation, 2021 In this paper we study the continuous and full discrete versions of a parabolic-parabolic-elliptic system with periodic terms that serves as a model for some chemotaxis phenomena. This model appears naturally in the interaction of two biological species and a chemical.
Mihaela Negreanu, A M Vargas
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Rigorous construction and classification of solitary-waves and exact soliton configurations in the nonlinear coupled Maccari system [PDF]
Scientific ReportsThe nonlinear coupled Maccari system, which is closely related to the Schrödinger equation, plays an important role in the modeling of nonlinear wave phenomena in areas such as deep-water wave theory, fluid dynamics, nonlinear optics, and plasma physics.
Akhtar Hussain +6 more
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Quasi-Periodic Solutions to Nonlinear PDEs
Series in Contemporary Applied Mathematics, 2019 We present recent developments in the theory of quasi-periodic solutions to nonlinear PDEs, such as the nonlinear Schrodinger and the nonlinear Klein-Gordon equations. These solutions hold in arbitrary dimensions, and the quasi-periodicity can be either in time or space.
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Regularity of time-periodic solutions to autonomous semilinear hyperbolic PDEs
Journal of Mathematical Analysis and Applications22 ...
Irina Kmit, Lutz Recke
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New solitary wave solutions to the coupled Maccari’s system
Results in Physics, 2021 The aim of this study is to find new exact solutions to the coupled Maccaris system by extended rational sine-cosine and rational sinh-cosh methods. By means of these methods, we found some fresh solitons of the above mentioned equation.
Javad Vahidi +5 more
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Alexandria Engineering Journal, 2023 In this article, we discuss various solitary wave solutions that are extremely important in applied mathematics. In order to construct accurate solution to nonlinear fractional PDEs, we have employed the Khater technique to nonlinear equation for 3 ...
Asghar Ali, Jamshad Ahmad, Sara Javed
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Open Physics, 2023 In this article, first integral method (FIM) is used to acquire the analytical solutions of (3+1)-D Wazwaz–Benjamin–Bona–Mahony and (2+1)-D cubic Klein–Gordon equation. New soliton solutions are obtained, such as solitons, cuspon, and periodic solutions.
Javeed Shumaila +4 more
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Results in Physics, 2023 In this paper, we study the extended (3+1)-dimensional nonlinear conformable Schrödinger equation with cubic–quintic nonlinearity. We use three different methods to obtain exact solutions of this equation: the G′/G expansion method, the extended ...
Mohammad Mirzazadeh +4 more
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