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Exact Solutions of Linear Partial Differential Equations with Variable Coefficients
Author(s) -
Sachdev P. L.,
Vaganan B. Mayil
Publication year - 1992
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1002/sapm1992873213
Subject(s) - mathematics , constant coefficients , variable (mathematics) , transformation (genetics) , partial differential equation , constant (computer programming) , mathematical analysis , linear differential equation , biochemistry , chemistry , computer science , gene , programming language
Bäcklund transformations relating the solutions of linear PDE with variable coefficients to those of PDE with constant coefficients are found, generalizing the study of Varley and Seymour [2]. Auto‐Bäcklund transformations are also determined. To facilitate the generation of new solutions via Bäcklund transformation, explicit solutions of both classes of the PDE just mentioned are found using invariance properties of these equations and other methods. Some of these solutions are new.