Solitary waves in the Ablowitz-Ladik equation with power-law nonlinearity

Abstract

We introduce a generalized version of the Ablowitz-Ladik model with a power-law nonlinearity, as a discretization of the continuum nonlinear Schrödinger equation with the same type of the nonlinearity. The model opens a way to study the interplay of discreteness and nonlinearity features. We identify stationary discrete-soliton states for different values of nonlinearity power $\sigma$, and address changes of their stability as frequency $\omega$ of the standing wave varies for given $\sigma$. Along with numerical methods, a variational approximation is used to predict the form of the discrete solitons, their stability changes, and bistability features by means of the Vakhitov-Kolokolov criterion (developed from the first principles). Development of instabilities and the resulting asymptotic dynamics are explored by means of direct simulations.

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Cited by in corpus (2)

• The closeness of localised structures between the Ablowitz-Ladik lattice and Discrete Nonlinear Schrödinger equations II: Generalised AL and DNLS systems
• Stability of compact breathers in translationally-invariant nonlinear chains with flat dispersion bands