We consider elastic grains which repel upon contact according to the Hertz potential V=aδn,n2, where δ is the overlap between adjacent grains and report numerical and analytical studies for the case of a 1-D chain of spherical grains to show that an impulse initiated at an end of a chain of...

We show that soliton interaction with finite-width inhomogeneities can activate a great number of soliton internal modes. We obtain the exact stationary soliton solution in the presence of inhomogeneities and solve exactly the stability problem. We present a Karhunen–Loève analysis of the...

We investigate the influence of long-range interactions on the energy localization in a one-dimensional Morse chain with an impurity by molecular dynamics simulations. The energy distribution around the impurity is studied. It shows that in the high temperature limit there is no difference upon...

In this work, we present an analytic study of the compactons structures in a class of nonlinear dispersive equations. The compactons: new form of solitary waves with compact support and width independent of amplitude, are formally constructed. We further establish solitary patterns solutions for...

We generalize the one-dimensional KdV equation for an inviscid incompressible irrotational fluid layer with free surface, finite depth, and finite boundary conditions. We study the nonlinear dynamics of a fluid of arbitrary depth in a bounded domain. By introducing a special relation between the...

In this paper, we would give a broad set of sufficient conditions of systems of linear partial differential equations which guarantee that the Grammian determinant solves the KP (Kadomtsev–Petviashvili) equation in the bilinear form. A systematic analysis of linear partial differential...