TY - JOUR
T1 - Flatons
T2 - Flat-top solitons in extended Gardner-like equations
AU - Rosenau, Philip
AU - Oron, Alexander
N1 - Publisher Copyright:
© 2020 Elsevier B.V.
PY - 2020/12
Y1 - 2020/12
N2 - 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.
AB - 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.
KW - Compactons
KW - Flatons
KW - Gardner Equation
KW - Solitons
UR - http://www.scopus.com/inward/record.url?scp=85087587634&partnerID=8YFLogxK
U2 - 10.1016/j.cnsns.2020.105442
DO - 10.1016/j.cnsns.2020.105442
M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???
AN - SCOPUS:85087587634
SN - 1007-5704
VL - 91
JO - Communications in Nonlinear Science and Numerical Simulation
JF - Communications in Nonlinear Science and Numerical Simulation
M1 - 105442
ER -