A novel softmax method for solving second Benney-Luke equation

IF 2.6 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics Pub Date : 2025-06-17 DOI:10.1016/j.cam.2025.116791

Nguyen Minh Tuan , Phayung Meesad

引用次数: 0

Abstract

This paper firstly introduces a novel approach utilizing the softmax method to solve the second Benney-Luke equation, specifically for the case where the parameter is equal to 2. Traditionally used in machine learning for classification tasks, the softmax function is applied here to derive exact solutions for this nonlinear partial differential equation. The method produces a variety of solution forms, including hyperbolic, trigonometric, and one-soliton solutions. These results offer valuable insights into the equation’s structure, expanding the understanding of wave phenomena on surface areas in mathematical physics, and contributing to the development of more comprehensive solution techniques for nonlinear wave equations.

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求解第二Benney-Luke方程的一种新的softmax方法

本文首先介绍了一种利用softmax方法求解第二个Benney-Luke方程的新方法，特别是在参数等于2的情况下。传统上用于分类任务的机器学习，这里应用softmax函数来推导这个非线性偏微分方程的精确解。该方法产生多种解形式，包括双曲解、三角解和单孤子解。这些结果为方程的结构提供了有价值的见解，扩展了对数学物理中表面波动现象的理解，并有助于发展更全面的非线性波动方程求解技术。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Computational and Applied Mathematics 数学-应用数学

CiteScore

5.40

自引率

4.20%

发文量

437

审稿时长

3.0 months

期刊介绍： The Journal of Computational and Applied Mathematics publishes original papers of high scientific value in all areas of computational and applied mathematics. The main interest of the Journal is in papers that describe and analyze new computational techniques for solving scientific or engineering problems. Also the improved analysis, including the effectiveness and applicability, of existing methods and algorithms is of importance. The computational efficiency (e.g. the convergence, stability, accuracy, ...) should be proved and illustrated by nontrivial numerical examples. Papers describing only variants of existing methods, without adding significant new computational properties are not of interest. The audience consists of: applied mathematicians, numerical analysts, computational scientists and engineers.