A nonconfocal involutive system and constrained flows associated with the MKdV[sub −] equation

2002 ◽  
Vol 43 (10) ◽  
pp. 4950 ◽  
Author(s):  
Yishen Li ◽  
Wen-Xiu Ma
Keyword(s):  
Involutive System

Integrability of Dispersionless Hirota-Type Equations and the Symplectic Monge–Ampère Property

2020 ◽  
Author(s):  
E V Ferapontov ◽  
B Kruglikov ◽  
V Novikov
Keyword(s):  
Type Equation ◽  
Lax Pair ◽  
Complete Classification ◽  
Conformal Structure ◽  
Characteristic Variety ◽  
Self Duality ◽  
Symmetry Properties ◽  
Monge Ampere ◽  
Involutive System

Abstract We prove that integrability of a dispersionless Hirota-type equation implies the symplectic Monge–Ampère property in any dimension $\geq 4$. In 4D, this yields a complete classification of integrable dispersionless partial differential equations (PDEs) of Hirota type through a list of heavenly type equations arising in self-dual gravity. As a by-product of our approach, we derive an involutive system of relations characterizing symplectic Monge–Ampère equations in any dimension. Moreover, we demonstrate that in 4D the requirement of integrability is equivalent to self-duality of the conformal structure defined by the characteristic variety of the equation on every solution, which is in turn equivalent to the existence of a dispersionless Lax pair. We also give a criterion of linearizability of a Hirota-type equation via flatness of the corresponding conformal structure and study symmetry properties of integrable equations.

scholarly journals The involutive system of higher-spin equations

2021 ◽  
Vol 964 ◽  
pp. 115325
Author(s):  
Rakibur Rahman
Keyword(s):  
Higher Spin ◽  
Involutive System

Relation between the Kadometsev–Petviashvili equation and the confocal involutive system

1999 ◽  
Vol 40 (8) ◽  
pp. 3948-3970 ◽  
Author(s):  
Cewen Cao ◽  
Yongtang Wu ◽  
Xianguo Geng
Keyword(s):  
Petviashvili Equation ◽  
Involutive System
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