Abstract
We present and study an extended Gardner-like family of equations, G(m,n;k):ut+(c+um−c−un)x+(uk)xxx=0,c±>0,n > m > 1, k ≥ 1, endowed with a non-convex convection which may be due to two opposing mechanisms that bound the range of velocities of both solitons and compactons beyond which they dissolve, and kink and/or antikink form. Close to solitons and compactons barrier, there is a narrow strip of velocities where the wave shape undergoes a structural change and rather than grow with velocity, their top flattens and they widen rapidly with minute changes in velocity. These waves, referred to as flatons, may be viewed as an approximate amalgam of a kink and anti kink placed at any distance from each other. Typical of solitons, once flatons form they are very robust with their domain of attraction being sensitive to the amplitude at which convection reverses its direction. A multi-dimensional extension of these equations unfolds a plethora of flatons which, unless m is even and n is odd, for every admissible velocity may span an entire sequence of multi-nodal radially symmetric flatons.
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 callMore From: Communications in Nonlinear Science and Numerical Simulation
Disclaimer: 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.
