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BRIEF RESEARCH REPORT article

Front. Phys.
Sec. Interdisciplinary Physics
Volume 13 - 2025 | doi: 10.3389/fphy.2025.1547245

New Solutions to a Category of nonlinear PDEs

Provisionally accepted
Bacui Li Bacui Li 1Fuzhang Wang Fuzhang Wang 2*
  • 1 Party School of CPC Fushun, Fushun, China
  • 2 Xuzhou University of Technology, Xuzhou, China

The final, formatted version of the article will be published soon.

    The nonlinear partial differential equations are not only used in many physical models, but also fundamentally applied in the field of nonlinear science. In order to solve certain nonlinear partial differential equation, the extended hyperbolic auxiliary equation method (EHAEM) is introduced in this article by means of the symbolic computation software. The basic idea of the new algorithm is that if certain nonlinear partial differential equation can be converted into the form of elliptic equation, then its solutions are readily obtained. By taking the generalized Schrödinger equation as an example, we demonstrate the effectiveness of the proposed algorithm. Meanwhile, many new solutions are worked out, which may be useful for depicting nonlinear physical phenomena.

    Keywords: Partial differential equation, Solitary wave solution, Jacobian elliptic function solution, Symbolic Computation Software, computerized mechanization

    Received: 18 Dec 2024; Accepted: 09 Jan 2025.

    Copyright: © 2025 Li and Wang. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

    * Correspondence: Fuzhang Wang, Xuzhou University of Technology, Xuzhou, China

    Disclaimer: All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article or claim that may be made by its manufacturer is not guaranteed or endorsed by the publisher.