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<p>The main objective of this paper is to investigate the equivalence problem for fifth-order differential operators on the line. We specifically focus on the case where the differential operators are subjected to general fiber-preserving transformations. To tackle this problem, we employ the Cartan method of equivalence via direct equivalence problem. This method allows us to determine whether two given differential operators are equivalent or not under a certain transformation. By applying this method, we are able to establish the conditions under which two fifth-order differential operators are equivalent under general fiber-preserving transformations. This provides us with a comprehensive understanding of the equivalence problem for these operators on the line. Overall, this paper contributes to the field of differential equations by shedding light on the equivalence problem for fifth-order operators and providing a systematic approach to analyze their equivalence under general fiber-preserving transformations.</p>

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Direct equivalence problem on fifth-order differential operator

  • 期刊论文

  • 发表日期：

    2025年5月14日

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  • Morteza Bakhshandeh,
  • Rohollah Bakhshandeh-Chamazkoti,
  • Mehdi Nadjafikhah

摘要

The main objective of this paper is to investigate the equivalence problem for fifth-order differential operators on the line. We specifically focus on the case where the differential operators are subjected to general fiber-preserving transformations. To tackle this problem, we employ the Cartan method of equivalence via direct equivalence problem. This method allows us to determine whether two given differential operators are equivalent or not under a certain transformation. By applying this method, we are able to establish the conditions under which two fifth-order differential operators are equivalent under general fiber-preserving transformations. This provides us with a comprehensive understanding of the equivalence problem for these operators on the line. Overall, this paper contributes to the field of differential equations by shedding light on the equivalence problem for fifth-order operators and providing a systematic approach to analyze their equivalence under general fiber-preserving transformations.