Nonlinear differential or difference equations are encountered not only in mathematics but
also in many areas of physics (evolution equations and propagation of a signal in an optical …

Abstract The Korteweg–de Vries, modified Korteweg–de Vries, and Harry Dym hierarchies of
integrable systems are shown to be equivalent to a hierarchy of chiral shape dynamics of …

The direct algebraic method for constructing travelling wave solutions on nonlinear evolution
and wave equations has been generalized and systematized. The class of solitary wave …

Exact implicit solutions with functional parameters of the (2+ 1)-dimensional Harry Dym (HD)
equation are constructed by the delta-dressing method. The interrelation between the HD …

The theory of bifurcations for dynamical system is employed to construct new exact solutions
of the generalized nonlinear Schrödinger equation. Firstly, the generalized nonlinear …

The automation of the traditional Painlevé test in Mathematica is discussed. The package
PainleveTest. m allows for the testing of polynomial systems of nonlinear ordinary and …

In this paper, the authors consider the Harry-Dym equation on the line with decaying initial
value. They construct the solution of the Harry-Dym equation via the solution of a 2× 2 matrix …

Solutions are reported for the problem of the motion of a two-dimensional interface between
a viscous and a nonviscous fluid. The solution has the interface moving uniformly while the …

We report a one-parameter family of solutions for the problem of the motion of an interface
between a viscous and a nonviscous two-dimensional fluid. The solutions have the interface …

In this work, we employ the inverse scattering approach to study the Poisson structure and
action-angle variables for the Harry-Dym equation. The Poisson brackets for the scattering …