We study the dynamics of a thin film over a substrate heated from below in a framework of a strongly nonlinear one-dimensional Cahn-Hilliard equation. The evolution leads to a fractalization into smaller and smaller scales. We demonstrate that a primitive element in the appearing hierarchical structure is a dissipative compacton. Both direct simulations and the analysis of a self-similar soluti...

The stability of the recently discovered compacton solutions is studied by means of both linear stability analysis as well as Lyapunov stability criteria. From the results obtained it follows that, unlike solitons, all the allowed compacton solutions are stable, as the stability condition is satisfied for arbitrary values of the nonlinearity parameter. The results are shown to be true even for ...

In this work, we study the Benjamin-Bona-Mahony like equations with a fully nonlinear dispersive term by means of the factorization technique. In this way we find the travelling wave solutions of this equation in terms of the Weierstrass function and its degenerated trigonometric and hyperbolic forms. Then, we obtain the pattern of periodic, solitary, compacton and kink-like solutions. We give ...

the extended homogeneous balance method is used to construct exacttraveling wave solutions of the maccari system, in which thehomogeneous balance method is applied to solve the riccati equationand the reduced nonlinear ordinary differential equation. many exacttraveling wave solutions of the maccari system equation aresuccessfully obtained.

In this work we consider model of asymmetric kinks, where the behavior solution in one side is different from other side. Also, models depend an integer $n$ and, with increase $n$, constructed kink assumes a hybrid character: compactlike profile on and kinklike We investigate numerically kink-antikink antikink-kink dynamics, aim to understand effect transition usual semi-compacton structure. Th...

An integrable 2-component Camassa-Holm 2-CH shallow water system is studied by using integral bifurcation method together with a translation-dilation transformation. Many traveling wave solutions of nonsingular type and singular type, such as solitary wave solutions, kink wave solutions, loop soliton solutions, compacton solutions, smooth periodic wave solutions, periodic kink wave solution, si...

A Hamiltonian formulation of nonlinear, parallel propagating, travelling whistler waves is developed. The complete system of equations reduces to two coupled differential equations for the transverse electron speed u and a phase variable φ=φp − φe representing the difference in the phases of the transverse complex velocities of the protons and the electrons. Two integrals of the equations are o...