Hodograph solutions for the generalized dKP equation

Abstract

We investigate the integrable $(2+1)$-dimensional generalized dispersionless KP (GdKP) equation (or Manakov-Santinit system) from the Lax-Sato form. Several particular three-component reductions are considered so that the GdKP equation can be reduced to hydrodynamic systems. Then one can construct infinite exact solutions of GdKP by the generalized hodograph method.

19 pages

References in corpus (3)

• A hierarchy of integrable PDEs in 2+1 dimensions associated with 2 - dimensional vector fields
• On the dressing method for Dunajski anti-self-duality equation
• Generalized dKP: Manakov-Santini hierarchy and its waterbag reduction

Cited by in corpus (1)

• Integrability of the Manakov--Santini hierarchy