Exact Solutions of Linear Partial Differential Equations with Variable Coefficients

1992 ◽  
Vol 87 (3) ◽  
pp. 213-237 ◽  
Author(s):  
P. L. Sachdev ◽  
B. Mayil Vaganan
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Exact Solutions ◽  
Variable Coefficients ◽  
Partial Differential ◽  
Linear Partial Differential Equations

scholarly journals Using the Differential Transform Method to Solve Non-Linear Partial Differential Equations

2020 ◽  
pp. 34-43
Author(s):  
Fadwa A. M. Madi ◽  
Fawzi Abdelwahid
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Exact Solutions ◽  
Variable Coefficients ◽  
Differential Transform Method ◽  
Partial Differential ◽  
Transform Method ◽  
Linear Partial Differential Equations ◽  
Differential Transform ◽  
Non Linear

In this work, we reviewed the two-dimensional differential transform, and introduced the differential transform method (DTM). As an application, we used this technique to find approximate and exact solutions of selected non-linear partial differential equations, with constant or variable coefficients and compared our results with the exact solutions. This shows that the introduced method is very effective, simple to apply to linear and nonlinear problems and it reduces the size of computational work comparing with other methods.

Lump and interaction solutions to linear PDEs in 2+1 dimensions via symbolic computation

2019 ◽  
Vol 33 (36) ◽  
pp. 1950457 ◽  
Author(s):  
Wen-Xiu Ma
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Exact Solutions ◽  
Symbolic Computation ◽  
Rogue Wave ◽  
Soliton Solutions ◽  
Partial Differential ◽  
Interaction Solutions ◽  
Linear Partial Differential Equations ◽  
Linear Pdes

The aim of this paper is to show that there exist lump solutions and interaction solutions to linear partial differential equations in 2[Formula: see text]+[Formula: see text]1 dimensions. Through symbolic computations with Maple, we exhibit a great variety of exact solutions to a class of (2[Formula: see text]+[Formula: see text]1)-dimensional linear partial differential equations, and present a specific example which possesses lump, lump-kink and lump-soliton solutions. This supplements the study on lump, rogue wave and breather solutions and their interaction solutions to nonlinear integrable equations.

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