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Zhang, Q., Xiong, M. and Chen, L. (2020) Exact Solutions of Two Nonlinear Partial Differential Equations by the First Integral Method. Advances in Pure Mathematics, 10, 12-20.
https://doi.org/10.4236/apm.2020.101002

has been cited by the following article:

• TITLE: On the Construction and Classification of the Common Invariant Solutions for Some P(1,4) -Invariant Partial Differential Equations

  AUTHORS: Vasyl M. Fedorchuk, Volodymyr I. Fedorchuk

  KEYWORDS: Symmetry Reduction, Classification of Invariant Solutions, Common Invariant Solutions, The Eikonal Equations, The Euler-Lagrange-Born-Infeld Equations, The Monge-Ampère Equations, Classification of Lie Algebras, Nonconjugate Subalgebras, Poincaré Group P(1, 4)

  JOURNAL NAME: Applied Mathematics, Vol.14 No.11, November 9, 2023

  ABSTRACT: We consider the following (1 + 3)-dimensional P(1,4)-invariant partial differential equations (PDEs): the Eikonal equation, the Euler-Lagrange-Born-Infeld equation, the homogeneous Monge-Ampère equation, the inhomogeneous Monge-Ampère equation. The purpose of this paper is to construct and classify the common invariant solutions for those equations. For this aim, we have used the results concerning construction and classification of invariant solutions for the (1 + 3)-dimensional P(1,4)-invariant Eikonal equation, since this equation is the simplest among the equations under investigation. The direct checked allowed us to conclude that the majority of invariant solutions of the (1 + 3)-dimensional Eikonal equation, obtained on the base of low-dimensional (dimL ≤ 3) nonconjugate subalgebras of the Lie algebra of the Poincaré group P(1,4), satisfy all the equations under investigation. In this paper, we present obtained common invariant solutions of the equations under study as well as the classification of those invariant solutions.