Abstract
A nonlocal nonlinear evolution equation is proposed that describes pulse formation in a dissipative system. A novel feature of the equation is that it can be solved exactly through a linearization procedure. The solutions are constructed under appropriate initial and boundary conditions and their properties are investigated in detail. Of particular interest is pulse formation, which is caused by a balance between nonlinearity and dissipation. The asymptotic behavior of the solution for large time is then represented by a train of moving pulses with equal amplitudes. The corresponding position of each pulse is shown to be characterized by the zero of the Hermite polynomial, irrespective of initial conditions.
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.
