The Lump, multi-wave, breather, interactional solutions and stability analysis for the general
r-th dispersionless Dym equation are obtained by some fruitful transformations. This …

The present study is devoted to obtaining some exact generalized solutions and new solitary
wave solutions for a (2+ 1)-dimensional nonlinear r th dispersionless Dym (rdDym) equation …

For several classes of second-order dispersionless PDEs, we show that the symbols of their
formal linearizations define conformal structures that must be Einstein-Weyl in 3D (or self …

The purpose of this article is to discuss an algebraic method for studying integrable
differential-difference lattices with two discrete and one continuous independent variables …

Let u be a function of n independent variables x1,…, xn, and let U=(uij) be the Hessian
matrix of u. The symplectic Monge–Ampère equation is defined as a linear relation among …

We present a simple novel construction of recursion operators for integrable
multidimensional dispersionless systems that admit a Lax pair whose operators are linear in …

In this study, we successfully apply Hirota's bilinear method (HBM) to retrieve the different
wave structures of the general r th dispersionless Dym equation by considering the test …

We use the Lie group method to investigate a one-dimensional optimal system of Lie
subalgebra for a (2+ 1)-dimensional rdDym equation. The new closed form solutions of the …

We consider a Lie algebra generalizing the Virasoro algebra to the case of two space
variables. We study its coadjoint representation and calculate the corresponding Euler …

The integrability of an m-component system of hydrodynamic type, ut= V (u) ux, by the
generalized hodograph method requires the diagonalizability of the m× m matrix V (u). This …