KAJIAN TENTANG LAX PAIR DAN PENERAPANNYA PADA PERSAMAAN LIOUVILLE

Authors

  • Andreno Juanda

DOI:

https://doi.org/10.25077/jmu.6.1.58-65.2017

Abstract

Abstrak. Lax pair merupakan pasangan dua operator diferensial yang jika disubstitusikan
ke suatu persamaan (dinamakan persamaan Lax) akan menghasilkan suatu persamaan
diferensial parsial tertentu. Jika suatu persamaan diferensial parsial memiliki
Lax pair, maka hal itu mengindikasikan bahwa persamaan diferensial tersebut bersifat
integrable. Dalam makalah ini akan dibahas analisis Lax pair secara umum, baik dalam
bentuk operator L dan M maupun dalam bentuk matriks X dan T. Selain itu juga dibahas
penerapan Lax pair secara khusus pada persamaan Liouville dengan mengkonrmasi
sifat-sifat terkait.

Kata Kunci: Persamaan diferensial, Lax pair, Persamaan Liouville

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Published

01-02-2017

Issue

Vol. 6 No. 1 (2017)

Section

Articles

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