We study the appearance of compacton-like solutions within the hydrodynamic-type model taking into account effects of spatial non-locality PACS codes: 02.30.Jr; 47.50.Cd; 83.10.Gr

Extending a Padé approximant method used for studying compactons in the Rosenau-Hyman (RH) equation, we study the numerical stability of single compactons of the Cooper-Shepard-Sodano (CSS) equation and their pairwise interactions. The CSS equation has a conserved Hamiltonian which has allowed various approaches for studying analytically the nonlinear stability of the solutions. We study three ...

We introduce a new dispersion-velocity particle method for approximating solutions of linear and nonlinear dispersive equations. This is the first time in which particle methods are being used for solving such equations. Our method is based on an extension of the diffusion-velocity method of Degond and Mustieles (SIAM J. Sci. Stat. Comput. 11(2), 293 (1990)) to the dispersive framework. The mai...

Solitons play a fundamental role in the evolution of general initial data for quasilinear dispersive partial differential equations, such as the Korteweg-de Vries (KdV), nonlinear Schrödinger, and the Kadomtsev-Petviashvili equations. These integrable equations have linear dispersion and the solitons have infinite support. We have derived and investigate a new KdV-like Hamiltonian partial diffe...

We study the properties of compacton-anticompacton collision processes. We compare and contrast results for the case of compacton-anticompacton solutions of the K(l,p) Rosenau-Hyman (RH) equation for l = p = 2, with compacton-anticompacton solutions of the L(l,p) Cooper-Shepard-Sodano (CSS) equation for p = 1 and l = 3. This study is performed using a Padé discretization of the RH and CSS equat...

By using the integral bifurcation method, we study the nonlinearK m,n equation for all possible values of m and n. Some new exact traveling wave solutions of explicit type, implicit type, and parametric type are obtained. These exact solutions include peculiar compacton solutions, singular periodic wave solutions, compacton-like periodic wave solutions, periodic blowup solutions, smooth soliton...

We argue that topological compactons (solitons with compact support) may be quite common objects if k-fields, i.e., fields with nonstandard kinetic term, are considered, by showing that even for models with well-behaved potentials the unusual kinetic part may lead to a power-like approach to the vacuum, which is a typical signal for the existence of compactons. The related approximate scaling s...