Results 1 to 10 of about 52,350 (200)
Applications of Solvable Lie Algebras to a Class of Third Order Equations
Mathematics, 2022 A family of third-order partial differential equations (PDEs) is analyzed. This family broadens out well-known PDEs such as the Korteweg-de Vries equation, the Gardner equation, and the Burgers equation, which model many real-world phenomena. Furthermore,
María S. Bruzón +3 more
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Reductions and Exact Solutions of Nonlinear Wave-Type PDEs with Proportional and More Complex Delays
Mathematics, 2023 The study gives a brief overview of publications on exact solutions for functional PDEs with delays of various types and on methods for constructing such solutions.
Andrei D. Polyanin, Vsevolod G. Sorokin
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General solutions of the Laplace equation
Partial Differential Equations in Applied Mathematics, 2022 With the purpose of concisely and effectively obtaining the general or exact solutions of partial differential equations (PDEs), we put forward some universal Z1transformations in present paper.
Hong Lai Zhu
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Buckling Analysis of Nano Composite Plates Based on Combination of the Incremental Load Technique and Dynamic Relaxation Method [PDF]
Mechanics of Advanced Composite Structures, 2021 In this paper, a different method, incremental load technique in conjunction with dynamic relaxation (DR) method, is employed to analyze the buckling behavior of composite plates reinforced with functionally graded (FG) distributions of single-walled ...
Vahid Zeighami, M.E. Golmakani
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Nonlinear Pantograph-Type Diffusion PDEs: Exact Solutions and the Principle of Analogy
Mathematics, 2021 We study nonlinear pantograph-type reaction–diffusion PDEs, which, in addition to the unknown u=u(x,t), also contain the same functions with dilated or contracted arguments of the form w=u(px,t), w=u(x,qt), and w=u(px,qt), where p and q are the free ...
Andrei D. Polyanin, Vsevolod G. Sorokin
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Mathematics, 2022 The study considers a nonlinear multi-parameter reaction–diffusion system of two Lotka–Volterra-type equations with several delays. It treats both cases of different diffusion coefficients and identical diffusion coefficients.
Andrei D. Polyanin, Alexei I. Zhurov
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Families of Solutions of Multitemporal Nonlinear Schrödinger PDE
Mathematics, 2021 The multitemporal nonlinear Schrödinger PDE (with oblique derivative) was stated for the first time in our research group as a universal amplitude equation which can be derived via a multiple scaling analysis in order to describe slow modulations of the ...
Cristian Ghiu +2 more
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On the analyticity of solutions of first-order nonlinear PDE [PDF]
Transactions of the American Mathematical Society, 1992 (From the author's abstract:) Let \(x\in R^ m\), \(t\in R^ 1\) and \(u\in C^ 2\). We discuss local and microlocal analyticity for solutions \(u\) to the nonlinear equation \(u_ t=f(x,t,u,u_ x)\). Here \(f(x,t,\zeta_ 0,\zeta)\) is complex valued and analytic in all arguments. We also assume \(f\) to be holomorphic in \((\zeta_ 0,\zeta)\in C\times C^ m\).
Hanges, Nicholas, Treves, François
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Mathematics, 2022 The generalized Logistic function that solves a first-order nonlinear ODE with an arbitrary positive power term of the dependent variable is introduced in this paper, by means of which the traveling wave solutions of a class of nonlinear evolution ...
Lingxiao Li +2 more
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Results in Physics, 2021 In the present article, we present for the first time optimal auxiliary function method (OAFM) for partial differential equation (PDEs). To find efficient and precision the proposed method, we take Lax’s seventh order korteweg-de Vries (KdV) and seventh ...
Laiq Zada +5 more
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