scholarly journals A Lax representation for the Born-Infeld equation

1998 ◽  
Vol 426 (1-2) ◽  
pp. 57-63 ◽  
Author(s):  
J.C. Brunelli ◽  
Ashok Das
Keyword(s):  
Lax Representation

scholarly journals ON THE INTEGRABILITY OF A CLASS OF MONGE–AMPÈRE EQUATIONS

2001 ◽  
Vol 13 (04) ◽  
pp. 529-543 ◽  
Author(s):  
J. C. BRUNELLI ◽  
M. GÜRSES ◽  
K. ZHELTUKHIN
Keyword(s):  
Sigma Models ◽  
Minimal Surfaces ◽  
Second Order ◽  
Lax Representation ◽  
Parameter Equation ◽  
Monge Ampere ◽  
Two Parameter

We give the Lax representations for the elliptic, hyperbolic and homogeneous second order Monge–Ampère equations. The connection between these equations and the equations of hydrodynamical type give us a scalar dispersionless Lax representation. A matrix dispersive Lax representation follows from the correspondence between sigma models, a two parameter equation for minimal surfaces and Monge–Ampère equations. Local as well nonlocal conserved densities are obtained.

scholarly journals Lax Pairs and First Integrals for Autonomous and Non-Autonomous Differential Equations Belonging to the Painlevé – Gambier List

2020 ◽  
Vol 16 (4) ◽  
pp. 637-650
Author(s):  
P. Guha ◽  
◽  
S. Garai ◽  
A.G. Choudhury ◽  
◽  
...  
Keyword(s):  
Differential Equations ◽  
First Integral ◽  
Lax Pair ◽  
First Integrals ◽  
Second Order ◽  
Lax Representation ◽  
Lax Pairs ◽  
Second Order Differential Equations ◽  
Autonomous Version ◽  
Autonomous Differential Equations

Recently Sinelshchikov et al. [1] formulated a Lax representation for a family of nonautonomous second-order differential equations. In this paper we extend their result and obtain the Lax pair and the associated first integral of a non-autonomous version of the Levinson – Smith equation. In addition, we have obtained Lax pairs and first integrals for several equations of the Painlevé – Gambier list, namely, the autonomous equations numbered XII, XVII, XVIII, XIX, XXI, XXII, XXIII, XXIX, XXXII, XXXVII, XLI, XLIII, as well as the non-autonomous equations Nos. XV and XVI in Ince’s book.

A Lax representation for the vertex operator and the central extension

1995 ◽  
Vol 171 (3) ◽  
pp. 547-588 ◽  
Author(s):  
M. Adler ◽  
T. Shiota ◽  
P. van Moerbeke
Keyword(s):  
Vertex Operator ◽  
Central Extension ◽  
Lax Representation
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