The Lissajous transformation is extended to any finite combination of harmonic oscillators and for any resonance mode. An example shows how normalization after a Lissajous transformation leads to a geometric characterization of the reduced phase space.

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...