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Vector shock soliton and the Hirota bilinear method
The Hirota bilinear method is applied to find an exact shock soliton solution of the system reaction-diffusion equations for n-component vector order parameter, with the reaction part in form of the third order polynomial, ...
On a 2+1-dimensional Whitham-Broer-Kaup system: A resonant NLS connection
It is established that the Whitham-Broer-Kaup shallow water system and the "resonant" nonlinear Schrödinger equation are equivalent. A symmetric integrable 2+1-dimensional version of the Whitham-Broer-Kaup system is ...
Variations on a theme of q-oscillator
(IOP Publishing, 2015-07-01)
We present several ideas in the direction of physical interpretation of q- and f-oscillators as nonlinear oscillators. First we show that an arbitrary one-dimensional integrable system in action-angle variables can be ...
Q-Shock soliton evolution
By generating function based on Jackson's q-exponential function and the standard exponential function, we introduce a new q-analogue of Hermite and Kampe-de Feriet polynomials. In contrast to q-Hermite polynomials with ...