﻿ Calculation of Soliton solutions：Solitary wave：Korteweg–de Vries equation(KdV equation)：Solution with one Soliton

# Calculation of Soliton solutions：Solitary wave：Korteweg–de Vries equation(KdV equation)：Solution with one Soliton

 1 Arbitrary constant：x0 - 2 Phase speed：c c＞0 - 3 Space：x - 4 Time：t - 5 Graph x- u(x,t) -
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## LaTex

$\frac{\partial u}{\partial t}+6u\frac{\partial u}{\partial x}+\frac{\partial^{3} u}{\partial x^{3}}=0, u(x,t)=f(x-ct)=\frac{c}{2}\textup{sech}^{2}(\frac{\sqrt{c}}{2}(x-ct-x_{0}))\, (c\gg 0)$

## Keyword

Soliton solutions,Solitary wave,Korteweg–de Vries equation(KdV equation),Solution with one Soliton,Arbitrary constant,Phase speed.

## Reference

[1]：Graham Woan著・堤正義訳：『ケンブリッジ物理公式ハンドブック』,共立出版,p.186,2007.
[2]：P. G. Drazin,R. S. Johnson：『Solitons: an introduction』,Cambridge University Press,p.22,1989
[3]：Korteweg–de Vries equation

## Remarks

・x0：Arbitrary constant
・c：Phase speed
・x：Space
・t：Time
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