New analytical soliton solutions to Korteweg-de Vries (KdV) equation using a family of hyperbolic tangent functions

Authors

  • Aria Buenaventura ⋅ PH Department of Physics, Ateneo de Manila University
  • Benjamin B. Dingel ⋅ US Nasfine Photonics Inc., Painted Post, NY, USA
  • Clyde J. Calgo ⋅ PH Department of Physics, Ateneo de Manila University

Abstract

We report a new and richer ansatz for the standard KdV equation. It is a variant of the hyperbolic tangent function and is governed by a new parameter p (0 < p ≤ 1). It leads to three important consequences: (i) when p = 1, our new ansatz reduces to the familiar tanh(𝜃) function that is used to construct the ideal sech-shaped soliton solution in the KdV equation, (ii) when p = 0, it shrinks to a scaled tanh(𝜃/2) function that has interesting features, and (iii) when p is between 0 and 1, it generates a family of new soliton solutions that can account for physical differences from an ideal sech-shaped soliton. This leads to three unique capabilities. First, it offers an accurate and flexible model for a more realistic soliton description. Second, it has better parameter curve fitting properties for given experimental data. Third, it produces a soliton solution where its width and speed can be tuned by the value of the parameter p.

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Issue

Article ID

SPP-2020-2G-01

Section

Theoretical and Mathematical Physics (Short Presentations)

Published

2020-10-19

How to Cite

[1]
A Buenaventura, BB Dingel, and CJ Calgo, New analytical soliton solutions to Korteweg-de Vries (KdV) equation using a family of hyperbolic tangent functions, Proceedings of the Samahang Pisika ng Pilipinas 38, SPP-2020-2G-01 (2020). URL: https://proceedings.spp-online.org/article/view/SPP-2020-2G-01.