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Solutions of Smooth Nonlinear Partial Differential Equations [PDF]
Abstract and Applied Analysis, 2011 The method of order completion provides a general and type-independent theory for the existence and basic regularity of the solutions of large classes of systems of nonlinear partial differential equations (PDEs). Recently, the application of convergence
Jan Harm van der Walt
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Study of coupled nonlinear partial differential equations for finding exact analytical solutions. [PDF]
R Soc Open Sci, 2015 Khan K, Akbar MA, Koppelaar H.
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Demonstratio Mathematica, 2021 In this work, we develop and analyze an explicit finite volume scheme for a one-dimensional nonlinear, degenerate, convection–diffusion equation having application in petroleum reservoir.
Mostefai Mohamed Lamine +2 more
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Nonlinear Partial Differential Equations [PDF]
, 2012 In this chapter we consider geometric partial differential equations, which appear for two-dimensional surfaces in their state of equilibrium. Here we give the differential-geometric foundations in Section 1 and determine in Section 2 the Euler equations of 2-dimensional, parametric functionals. In Section 3 we present the theory of characteristics for
Luis A. Caffarelli +4 more
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Solutions of Nonlinear Integro-Partial Differential Equations by the Method of G′/G,1/G
Advances in Mathematical Physics, 2022 In this article, a special expansion method is implemented in solving nonlinear integro-partial differential equations of 2+1-dimensional using a special expansion method of G′/G,1/G.
Daba Meshesha Gusu, Chala Bulo
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International Journal of Differential Equations, 2021 In this paper, a novel analytical method for solving nonlinear partial differential equations is studied. This method is known as triple Laplace transform decomposition method. This method is generalized in the sense of conformable derivative.
Shailesh A. Bhanotar +1 more
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Axioms, 2023 Transformations are much used to connect complicated nonlinear differential equations to simple equations with known exact solutions. Two examples of this are the Hopf–Cole transformation and the simple equations method.
Nikolay K. Vitanov
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A method for constructing a complete bifurcation picture of a boundary value problem for nonlinear partial differential equations: application of the Kolmogorov-Arnold theorem [PDF]
Известия высших учебных заведений: Прикладная нелинейная динамикаThe purpose of this study is to develop a numerical method for bifurcation analysis of nonlinear partial differential equations, based on the reduction of partial differential equations to ordinary ones, using the Kolmogorov-Arnold theorem.
Gromov, Vasily Alexandrovich +4 more
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On a linear system of differential equations
Вестник КазНУ. Серия математика, механика, информатика, 2019 The linear systems of partial differential equations of the first order with the identical main parts is considered. Аpplying the well-known relation between a normal system of ordinary differential equations and a linear system of partial differential
T. М. Aldibekov, M. M. Aldazharova
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Известия высших учебных заведений. Поволжский регион: Физико-математические науки, 2020 Background. Finding exact solutions of nonlinear partial differential equations is one of the main problems of the nonlinear systems theory. A number of methods have been developed for integrable systems, but due to the complexity of various nonlinear
T. V. Red'kina, O. V. Novikova
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