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A Brief History of Solitons and the KDV Equation


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1 Department of Mathematics, College of Charleston, Charleston, SC 29424, United States
 

Soliton theory is an interdisciplinary area at the interface of mathematics and physics. It studies a special class of nonlinear partial differential equations (NLPDEs) having solutions that are waves which behave like particles. Amazingly, unlike most NLPDEs, we can write exact formulas for the solutions to these ‘soliton equations’. This article is a review providing the historical context necessary to appreciate these spectacular developments, a brief overview of the early history of the field, and a list of references to consult for additional information.

Keywords

KDV Equation, Nonlinear Partial Differential Equation, Solitons, Waves.
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  • A Brief History of Solitons and the KDV Equation

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Authors

Alex Kasman
Department of Mathematics, College of Charleston, Charleston, SC 29424, United States

Abstract


Soliton theory is an interdisciplinary area at the interface of mathematics and physics. It studies a special class of nonlinear partial differential equations (NLPDEs) having solutions that are waves which behave like particles. Amazingly, unlike most NLPDEs, we can write exact formulas for the solutions to these ‘soliton equations’. This article is a review providing the historical context necessary to appreciate these spectacular developments, a brief overview of the early history of the field, and a list of references to consult for additional information.

Keywords


KDV Equation, Nonlinear Partial Differential Equation, Solitons, Waves.

References





DOI: https://doi.org/10.18520/cs%2Fv115%2Fi8%2F1486-1496