Solutions of Second Order Hyperbolic Differential Equations with Constant Coefficients in a Domain with a Plane Boundary

Fritz John ◽  
1985 ◽  
pp. 267-291
Author(s):  
Fritz John
Keyword(s):  
Differential Equations ◽  
Second Order ◽  
Plane Boundary ◽  
Constant Coefficients ◽  
Hyperbolic Differential Equations

Cauchy problems for second order hyperbolic differential equations with constant coefficients

1983 ◽  
Vol 26 (3) ◽  
pp. 307-311 ◽  
Author(s):  
J. S. Lowndes
Keyword(s):  
Wave Equation ◽  
Differential Equations ◽  
Fractional Calculus ◽  
Second Order ◽  
Cauchy Problems ◽  
Order Linear ◽  
Constant Coefficients ◽  
Darboux Equation ◽  
One To One ◽  
Hyperbolic Differential Equations

1. It is well known [1] that there is a one-to-one relation between solutions of the Darboux equation and the wave equation. The purpose of this paper is to show that some recent results in the fractional calculus can be used to obtain a similar connection between solutions of Darboux's equation and second order linear hyperbolic differential equations with constant coefficients.

scholarly journals On some solutions of second order hyperbolic differential equations with constant coefficients

1987 ◽  
Vol 29 (1) ◽  
pp. 69-72
Author(s):  
J. S. Lowndes
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Fractional Calculus ◽  
Second Order ◽  
Hyperbolic Differential Equation ◽  
Constant Coefficients ◽  
Image Position ◽  
Hyperbolic Differential Equations

If we seek solutions of the hyperbolic differential equationwhich depend only on the variables i and , we see that these solutions must be even in r and satisfy the differential equationThe object of this paper is to show that some recent results in the fractional calculus can be used to prove the following theorem.

scholarly journals Linearization of Two Second-Order Ordinary Differential Equations via Fiber Preserving Point Transformations

2011 ◽  
Vol 2011 ◽  
pp. 1-21 ◽  
Author(s):  
Sakka Sookmee ◽  
Sergey V. Meleshko
Keyword(s):  
Linear System ◽  
General Solution ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Necessary Conditions ◽  
Second Order ◽  
Point Transformations ◽  
Constant Coefficients ◽  
Linearizable System

The necessary form of a linearizable system of two second-order ordinary differential equations y1″=f1(x,y1,y2,y1′,y2′), y2″=f2(x,y1,y2,y1′,y2′) is obtained. Some other necessary conditions were also found. The main problem studied in the paper is to obtain criteria for a system to be equivalent to a linear system with constant coefficients under fiber preserving transformations. A linear system with constant coefficients is chosen because of its simplicity in finding the general solution. Examples demonstrating the procedure of using the linearization theorems are presented.

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