In this paper, a novel approach leveraging artificial neural networks is introduced to approximate solutions for partial differential equations. The one-dimensi ...

In this paper, lump solutions of nonlinear partial differential equations, the generalized (2 + 1)-dimensional KP equation and the Jimbo–Miwa equation, are studied by using the Hirota bilinear method ...

Basic training in Sobolev space theory and linear partial differential equations, for example as provided by MAT4305 – Partial Differential Equations and Sobolev Spaces I. Overlapping courses 10 ...

Basic training in Sobolev space theory and linear partial differential equations, for example as provided by MAT4305 – Partial Differential Equations and Sobolev Spaces I. Overlapping courses 10 ...

Cellular neural networks (CNNs)-a paradigm for locally connected analog array-computing structures-are considered for solving partial differential equations (PDE's) and systems of ordinary ...

This review begins with the standard Lie symmetry theory for nonlinear PDEs and explores extensions of symmetry analysis. First, it introduces three key symmetry reduction methods: the classical ...

In this work, we examine time-fractional fourth-order parabolic partial differential equations with the aid of the optimal homotopy asymptotic method (OHAM). The 2nd order approximate results obtained ...

This article describes a method that modifies the auxiliary differential equation methodology for solving nonlinear partial differential equations [18]. Over the past 30 years, fresh and ...

by International Conference on Nonlinear Partial Differential Equations and Applications (1998 : Northwestern University) Publication date 1999 Topics Differential equations, Nonlinear -- Congresses ...