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

  • Aria Buenaventura Ateneo de Manila University
  • Benjamin B. Dingel Nasfine Photonics Inc., Painted Post, NY, USA
  • Clyde J. Calgo 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.

Published
2020-09-06
How to Cite
[1]
A. Buenaventura, B. Dingel, and C. 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://paperview.spp-online.org/proceedings/article/view/SPP-2020-2G-01.
Section
2G/5A Theoretical and Mathematical Physics (Short Presentations)