We present and study a class of Lotka-Volterra chains with symmetric 2N-neighbors interactions. To identify the types of solitary waves which may propagate along the chain, we study their quasi-continuum approximations which, depending on the coupling between neighbors, reduce into a large variety of partial differential equations. Notable among the emerging equations is a bi-cubic equation ut = [bu2 + 2κuu + (uxx)2]x which we study in some detail. It begets remarkably stable topological and non-topological solitary compactons that interact almost elastically. They are used to identify discretons, their solitary discrete antecedents on the lattice, which decay at a doubly exponential rate. Many of the discrete modes are robust while others either decompose or evolve into breathers.
|Journal||Journal of Physics A: Mathematical and Theoretical|
|State||Published - 25 Jan 2016|
- bi-cubic pde
- extended Lotka-Volterra chains