Abstract
We compare the properties of generalized nonlinear Klein-Gordon equations with a sinusoidal coupling (sine-lattice equations) to those of the usual nonlinear Klein-Gordon equation with harmonic coupling for three equations leading to the same sine-Gordon equation in the continuum limit. Using Hirota's bilinear method we find a strong analogy between the properties of nonlinear oscillatory modes in the three equations. Numerical simulations confirm this analogy even for very discrete cases. However we point out a fundamental difference between the harmonic and sinusoidal coupling by exhibiting a new class of localized nonlinear excitations which are specific to the sinusoidal coupling, the rotating modes. They can be created thermally. An approximate analytical solution is obtained for these modes which are intrinsically discrete and appear to be extremely stable, even in collisions with breathers. Possible implications for physics are discussed.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
